Sometimes it seems to have no effect on the price, but other times it causes drastic price movements. Feel free to check it out and let me know what you think about it.
it is because Tether is not "causing" anything. the dates just happen to coincide cometimes. basically they mainly print more USDT whenever there is more usage for it and if you look at the whole market you can see that Tether is not just used for trading bitcoin, it is used for altcoins too. in fact one of the ways people escape altcoin dumps is to go to USDT. and looking at the charts for instance the March, May and June cases are 3 of the biggest altcoin dumps of this year where each altcoin went down at least 50% and a huge amount of money exited that market. many of it to USDT.
of course in some cases like during January Tether printing "caused" a rise but not because of the reasons you might think. the reason was because people were convinced Tether is "pumping" bitcoin so when they released new coins they started FOMO buying bitcoin to stay ahead of something that wasn't even happening so the price went up.