This is likely *way* more information than you want to know. Executive summary: Yes, more culture will make it acidify more quickly. Yes, it will affect the cheese. Yes, you can work with it, but it requires a fair amount of experience and attention to detail. What follows is the mental model I use every time I make cheese. It's kind of complicated, but I find it really helpful. I hope you will too.
The speed of acidification depends on: 1) the number of cells per ml of milk (more is faster), 2) the temperature (higher is faster) 3) the amount of food available (but in the period we're talking about there is always more than enough food). If you salt the milk, or something like that it can slow down the culture too, but let's not get into that.
So, yes, more culture will generally mean faster acidification. So you can lower the temperature to compensate... but... that's also going to affect how the curds will curdle and drain. So it's actually quite complicated.
My best cheese making piece of advice is to think about the time where you drain the whey from the curds (or take the curds out of the whey) as a target point. Your goal is to hit a specific pH (acidity) and a specific curd structure (size, moisture level). The acidity is based on the amount of culture, its health and the temperature. So while you are tracking that, you want to adjust how you are treating the curds.
I always do a flocculation test with my makes (float a milk cap/bottle cap in the milk and time how long it takes before you can't spin it any more -- that's the "flocculation time"). The total coagulation time should be a multiple of the "flocculation time". So if your recipe says you have a multiplier of 3.0 and you had a flocculation time of 12 minutes, then the total coagulation time (before you cut the curds) should be 36 minutes.
You should have an idea of what your goal flocculation time is. As long as you are using the same milk you normally use, you are using the same amount of rennet and you hit your temperature correctly, the speed of flocculation will be related to the speed that the milk is acidifying. You can use this as a kind of poor person's pH meter. If you are flocculating faster than you expect, it means you added too much culture. If it's slower, then you added too little culture. You should also check just before you cut the curds to make sure that the firmness is what you expect.
I won't write my normal rant about "clean break" -- just note that the desired firmness of the curd is different for every single type of cheese and should be related to the flocculation multiplier. A multiplier of 2.0 will be "sloppier" than 3.0. 4.0 will be much more firm than 3.0. You get the idea. Try to find recipes where they tell you the flocculation goal and the desired multiplier rather than the total coagulation time, although you can often figure it out yourself if you have experience. The drier the cheese, the lower the multiplier will be (and the more "sloppy" you want the break). You can look at the amount of rennet (often practically random in many recipes, unfortunately), the temperature and the amount of culture added and guess the flocculation target. Then you take the total coagulation time and divide by that to calculate the multiplier. I hope that makes sense... As you practice making cheese, you'll be adjusting your own recipes, so don't worry about it. Usually it takes me at least 5 times to make a good version of a new style of cheese for me. If you have that kind of expectation, you won't worry so much about "getting it right" the first time.
Anyway... If you realise you are going too fast or too slow (either by the flocculation and coagulation time, or by measuring the pH directly), you can simply cut the curds bigger or smaller. The smaller you cut the curds, the faster they will drain. So if you are acidifying faster than you want, cut the curds smaller so that you end up at the right consistency when you have to drain (due to reaching your pH target). If you are going slower, then cut the curds larger. Similarly, if you are acidifying very slowly, you can stir every minute or so instead of consistently. This helps you hit your target.
Another side note: If you are using poor quality milk (for instance homogenized milk) and you expect the curds to fracture a lot, add less culture so that it acidifies more slowly. This gives you a longer coagulation time, and you can take your time stirring so that the curds have more time to get stronger before you have to drain due to pH.
Of course, if you don't have a pH meter, you won't know when to drain via pH (because, honestly the whey at pH 6.3 tastes *exactly* like the whey at pH 6.0, unless you are some super tasting mutant). So keeping track of how the acidification is going and adjusting the way you treat your curds is the only way to know when you are done. Most recipes give you a stir time, but that's completely unreliable because your cheese is going to be totally different than the author's. You really need to go until the curds are at the consistency you want and hope that they are at the pH that you want.
Once you drain the curds and get them in the mold, you can see how easily the curds come together (the easier they hold together, the higher the pH -- less acidic). However, you can't really easily know this before you drain (well, taking some curds and doing a squeeze test can help, but I find it quite difficult). Again, it's important to take good notes and keep an attitude that you're going to figure out your process over a series of makes rather than nailing it on the first go.
The cheese will continue to acidify relatively quickly until you salt it. The amount of culture you added doesn't really make much difference at this point other than it will acidify more quickly as you are pressing it (and before you salt it). You just have to do all the steps more quickly, but generally you have more than enough time anyway. At worst, turn on the air conditioning to slow things down. The opposite is even easier to deal with because the only downside is that it takes longer to drain and acidify (which is a PITA if you are making a cheddar or pasta filata cheese, but doesn't really affect anything other than time).
After you salt it, the culture is still alive and it does slowly acidify the cheese, but there are lots of processes that tend to balance out the acidity unless you have excess whey (i.e. the cheese didn't drain properly, often because you overpressed it early).
As you can see, cheese making is a deep subject, but as complicated as all that probably seems, it's really not that bad once you get the hang of it.
