Why does it matter if your credit card gets picked up before your transit card? If there's a discount or pass on the transit card, seems like the agency should let you attach it to your credit cards instead of requiring you to get a separate card.
Buying a month pass is a tax benefited account for commuting. [At many work places]. On top of that you have different pricing and you aren't paying full price at tap.
The CC being picked up means you're paying the full fare immediently even if you have the pass on the other card.
