Oh the clicking problem was even worse for me, I avoided spending points on the seconds per click upgrades. It felt like a waste when I can just click faster. I only upgraded when my hand started hurting and I realised its importance, before limping to the end using my left hand for slow clicking and my right hand for the minigames.
As for the more frequent clicking, I think it's because of the way the timer works. Waiting 5 seconds between clicks means that if an activity pops up just before you click, you functionally have 5 less seconds on your timer. I think you could maybe fix this by allowing one more click after the activity spawns; allowing overflow when clicking (as in if you timer is 10 seconds and your per click is 5, and you click at 9, the timer does go up to 14, but you can't click again until its less than 10); or of course, implementing holding would also fix this.