These types of credits typically post as reconciliation on your credit card bill - thus the manner in which you verify payment (Apple Pay, Chip, swipe, etc.) does not matter.

The types of rules that will more likely trip you up on cards are not technicalities on payment authentication but instead on how the credits work. For example, some perks need to be activated before use (often the case with Amex perks), while others apply based on billing anniversary or don't credit until after your first year / billing anniversary.

The free bag perk and priority status are among the simpler ones - just make sure your United MileagePlus number is associated with your credit card. This is typically done in the credit card enrollment process (it would be required to earn miles anyway) but when you go to Chase.com and login in the top right section ("Rewards") under your chase points it should also show your United mileage balance if they are correctly linked.