The question is why, not what does the manual say?
The answer is that alpha and the P value are different things, and they work in opposite ways.
When you get a P value, you are asking "at what alpha value would I reject the null?". In other words, we are going to view our observed |t| as the critical value of the test, and the P value is the alpha that has that critical value.
So, given a particular adjusted P value, and given that it was adjusted based on the Bonferroni method, you would take that adjusted P as the borderline alpha level for the Bonferroni test; accordingly, you have to divide that adjusted P by the number of tests in order to obtain the corresponding borderline critical value from the t distribution.
Conversely, given the t ratio, then to get a P value, we view that t value as the borderline critical value. The unadjusted P value is the alpha for which that is at the borderline. To get the adjusted P value, we have to multiply the unadjusted P value by the number of tests so that it comes out right hen you later divide it, as described in the preceding paragraph.