a few yrs ago my USAir flight was Cxed out of EWR and I was FIMed over to UA, they too ended up CXing theirs and FIMed over to DL out of JFK and gave me a cab voucher, all I did was turn that over to teh driver and off we went. Didnt pay a cent more.
Im not sure what exactly took place with the OP and his Ride, but I always understood that the voucher given included everything to go to whatever destination it had down on it, in the OPs case LGA./ If that wasnt the case then the Carriers should get their act together
IMO at no time while using 1 of these vouchers should a person have to pay out any further funds for any reason, that includes not having to Tip the driver a sits all been worked out ahead of time with the Companys or the voucher should state on it Gratuitys not included and leave it up to the Rider if they wish to tip the driver
sounds to me either the Driver scammed the OP or didnt give the OP a voucher for the proper amount (which I find hard to believe since its prearranged)