yes we assume a 2 tailed t test. however you may have misunderstood something here.
so in a normal distribution for example, if it is a 95% confidence interval (i.e. 5% significance level), it means it is the z-score that leaves a probability of 2.5% (α/2) on the upper tail (right-hand tail) of the standard normal distribution. it isn’t 5% in each tail, but 5% in total, which means 2.5% in each tail.