It seems you have a variable formatted as datetime. If so, no need to convert to string. There are appropriate functions that allow you to manipulate the original variable. This is clearly explained in help datetime:
clear
set more off
*----- example data -----
set obs 5
gen double datet = _n * 100000000
format datet %tc
list
*----- what you want -----
gen double date = dofc(datet)
format %td date
gen double hour = hh(datet) + mm(datet)/60 + ss(datet)/3600
list
The reason you find your original result surprising is because you are not aware of the fact that underlying the datetime display format, is a numerical value.
A good read (aside from help datetime) is
Stata tip 113: Changing a variable's format: What it does and does not mean, The Stata Journal, by Nicholas J. Cox.
Edit
To answer your last question:
If you want to create an indicator variable marking pre/post periods, one way is using td() (see the help file). Following the example given above:
// before 04jan1960
gen pre = date < td(04jan1960)
Creating this indicator variable is not always necessary. Most commands allow the use of the if qualifier, and you can insert the condition directly. See help if.
If you mean something else, you should be more explicit.
describe.