Working on same table from different session

suppose I have following operation in a SP:

truncate table mytab

insert into mytab(...)

select ...

then if bot different user run this SP at same time(for example both start within less one second, but the SP need to run more then one second), the second user will remove the data for the first user or need to wait first user done the transaction?

Any conflict for this case?

I know if mytab is temp table like #mytab, there is no problem as each temp tab only visible for its session. but not sure about a physical table.