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What? 2 sigma means 2.5% at each end.
That sentence is imprecise.
If you divide a standard Gaussian at the +2 sigma boundary, the probability mass to the left will be 97.5% and to the right ("the tail") -- 2.5%.
So two sigmas don't mean 2.5% at each end, they mean 2.5% at one end.
On the other hand, if you use a 4-sigma interval from -2 sigmas to +2 sigmas, the probability mass inside that interval will be 95% and both tails together will make 5% or 2.5% each.