In most cases, yes, it is normal and typical to receive bites and even see Bed Bugs throughout #treatment.
Remember Bed Bug bites can take days to show up. You might wake up with new bites after treatment but they may not have occurred the night before.
Even if you do wake up with bites it is still normal to see them until your #pestcontrol company confirms that your problem has been solved.
In regards to seeing Bed Bugs, they are not a once and done process. You will at least need a follow up service and inspection to verify that everything has been eradicated.