Some confusion here. exec runs a separate program, possibly with arguments. source is not a separate program, it is another Tcl command which reads a file of Tcl commands and executes them, but does not pass arguments. If the other script you are trying to call is written to be run on from the command line, it will expect to find its arguments as a list in variable argv. You can fake this by setting argv to the list of arguments before running source, eg.
set argv {first_arg second_arg}
source script_path
Alternatively you could use exec to start a whole separate Tcl executable and pass it the script and arguments:
exec script_path first_arg second_arg