Paradox? setting up sampe size with alfa and beta error and analyzing it with t-test

There seems to be some strange things:
1) you want to set-up a Design of experiments: using statistics tools; size = 10 ; alfa = 0.05 ; difference 1 time the standard deviation ; -> power = 0.56 ; so this is a very poor power to see a difference when there acutally is one.

2)now you have actually a data set size 10, diffrence = 1 standard deviation; You perform a 2-sided t-test: the p-value is 0.038; lower than 0.05, so very statistical relevant.

...???a bit confusing.

This is because 1) you don't have the data and in 2) you do. If you don't have them, due to random events, the chances they overlap too much is too high?