Will only the assigned planes park there?
No, Parking assignments only create a preference for a parking spot.
There is no exclusion in FS parking except one - the aircraft is too large for the parking spot.
When you are seeing aircraft park in the wrong place - your parking assignments are not matching the AI flight plans on your computer.
AI Parking must match the flight plans, not the real world airport. AI flight plans for large airlines like Air Canada almost always have more aircraft overnight at their major hubs than there are gates for that airline in the real world.
This is easy for a real world airline, they just push the extra aircraft back to an empty area of the ramp - but FS won't move an AI aircraft on the ground after it is parked.
My recommendation for a hub airport is to set the traffic file so that only the major airline is active / visible.
Work the parking assignments until that airline parks perfectly at all times of the day.
Make sure every passenger carrying aircraft, even the regional props and jets, is atc_parking_types=GATE and every parking spot they are to use is GATE_HEAVY, GATE_MEDUIM or GATE_SMALL (Though in FSX, you may have to use RAMP_GA with and airline parking code for spots where you do not want the pushback tug, baggage cart and baggage loader to appear)
Check the parking an hour before dawn, at 8 am, 10 am , noon, 2 pm, 4 pm, 6 pm, 8 pm, 10 pm , midnight and 2 am.
Also be aware that your airline parking locations not at the terminal or jetway must be coded with so that the NAME in the parking spot properties is GATE + a letter is you have any GATE + a letter parking on the airport.
GATE without a letter has a priority over GATE with a letter.
There is no priority of GATE A over GATE B, etc.
I tend to use GATE R for overflow parking spots.
Once you have your main airline and it's regional feeders parking correctly - add all your cargo airlines and check again. That is the best way to check cargo parking - with only one major airline on the airport and lots of empty gate spots to asorb overflow.
You'll spot how much extra cargo parking you need quickly.
Then add other airlines - working for the ones with the most traffic down the list.
I always prefer 10-15% of the parking of each type on the airport have no parking code/ assignments. That lets you spot problems caused by changes in AI schedules pretty easily.
One other factor which you may or may not wish to do is to edit the AI flight plans and put the largest aircraft at the top of the flightplans file.
The normal practice seems to be the smaller aircraft first.
What that does is hide any issues you have with too few of the smallest spots and aircraft cascading into larger spots.
If the heavies are first in the plan, then the medium sized aircraft, then the small jets, then the regionals - you will see quickly if you don't have enough parking for a particular size aircraft.