Since your trip was last Sunday, let us know how it went.
For future drivers... they will bill you.
You need to make sure you cross in the carpool lane to get the discounted toll.
If you had a transponder you can drive for free in the express lanes.
Per
Clean Air Vehicles - FasTrak...
To use an express lane with your CAV you must use a FasTrak Flex or FasTrak CAV toll tag.
I-880 and SR-237: If you have 3+ people in your vehicle and are using a FasTrak Flex or FasTrak CAV toll tag, set the switch to position 3+ to travel toll free.
I-580: FasTrak Flex or FasTrak CAV toll tag, eligible CAVs can travel in the express lanes toll free regardless of the number of passengers in the vehicle. If you are using a FasTrak Flex toll tag, be sure to switch to position 2 or position 3+ on your toll tag.
I-680 Contra Costa: If you have two or more people in your vehicle and are using a FasTrak Flex or FasTrak CAV toll tag, set the switch to position 2 or 3+ to travel toll free.
I-680 Sunol: Eligible CAVs can travel in the I-680 Sunol express lane toll free, regardless of the number of passengers. A FasTrak toll tag is not necessary. If you have a FasTrak CAV or Flex toll tag, set it to position 2 or position 3+ to avoid being charged.