WIth that interpretation, you couldn't have a halt at a nonstandard time without halting at some standard time, right? If it were halted at some nonstandard time, it would be halted at almost all the standard times in that nonstandard time (here "almost all" is with respect to the chosen ultrafilter), and hence in particular at some standard time.

(Add here standard note for readers unused to infinity that it can be made perfectly sensible to talk about Turing machines running infinitely long and beyond but this has nothing to do with what's being talked about here.)