I believe they want the pump running is to make sure the salt is fully in suspension. At least here they always say wait 24 hours before starting the swg after adding salt.
CYA you can add when full. Best to get dry granular. Put it in an old sock and hang by the return. Squeeze it occasionally to help it. I usually spend 15 minutes or so squeezing about 1 or 2 lbs out. Be careful and not add too much CYA. Start with either half or 2/3 of what you think you need. If you go too high the only recourse is to partially drain the pool and refill.
I would add some chlorine right away if you can, enough for about 5ppm. The swg will create small amounts but will struggle to get the FC high enough, soon enough.
IF it is warm enough, they can swim tomorrow once you get the cya dissolved and some chlorine in it. They can swim 30 minutes after most chemical additions.
What type of test kit do you have? You will need either the TF100 or the Taylor K-2006C to do a proper job and follow TFP methods.
Check out ABC's of pool water chemistry in Pool school.