Exposure is one. The more you train and encounter this issue the more your mind can get used to it and filter out the stuff that makes you panic.
As mentioned above, intensity is important, too. It's not wrong to be quick on the ball, but being quick on the bounce and putting a lot of intensity in the shot is high risk. When you're taking a ball really quickly, you actually have more time to make a slower, well placed shot (and usually more angle to do so, too). Digging in early, especially when this feels natural to you, is a very good play, highly disturbing especially when you put 4-5 balls back on the table quickly.
If your problem is in trying to outbalance your opponent, yet getting surprised by their spin, well you need to improve your spin reading.
If your problem is in trying to outbalance your opponent and then missing your big finisher, the answer might be to stop trying to hit big finishers. Just outplace them in an impossible corner when they're off balance. Sure, it's physically less satisfying in the short term, but getting the upper hand even against big attackers will feel very nice in the long term I promise.