Thanks for the detailed reply. What can I say: way too complicated and designed to alienate tourists (this is assuming that locals know about all this).
It would be unfair to say that this system will keep me from visiting Chicago in the future, but it certainly doesn't make me want to visit again in the future either. A clear case of penny-wise and pound-foul decision making on part of the public transport agencies.
You say transfers from CTA to Pace and vice versa are allowed when paying a single-ride fare. I guess no transfers are allowed when transfering from 250 to 270? I was charged the single fare ($1.75) twice.
HTB.
Yes, transfers are allowed between Pace buses, but only when you pay with a Ventra account. (The same applies to transfers between CTA/Pace or CTA/CTA.) You paid with your credit card. This is referred to "Pay as You Go" or PAYG. If you had added at least $2 in Transit Value to your credit card at the Ventra Vending Machine in addition to the 3-day pass, you would have been charged $2 for the two rides ($1.75 for the initial ride plus $.25 for the transfer). You apparently had only the 3-day pass in your account and did not have any Transit Value.
You apparently know how to use the Ventra Vending Machine, but for the benefit of anyone else reading, here is how to add Transit Value to your personal credit card:
https://www.youtube.com/watch?v=df-elixixB0
The idea is if you "prepay" your fare (i.e. add Transit Value) you get transfers. If they have to charge your credit card at the time you tap it on the card reader, you don't. (Buses still accept cash and if you pay in cash you don't get transfers either.)
The system is absurdly complex. We have to deal with it everyday. You're lucky you only needed to deal with it for a few days.