Exchange1 would know the output (call it Out1) that it has given to Adr1. When Out1 is spent, Exchange2 (if sharing knowledge through backchannels with Exchange1) will see that there is a 1 in N chance that Out1 has been spent in a transaction with Exchange2, where N is the ring size that was used.
Exchange1 knows the exact amount of Out1, since it gave it to Adr1. So if it was an uncommon amount, and that exact amount was cashed out with Exchange2 (minus the transaction fee), then it'd be a pretty good guess that Out1 was being spent at Exchange2 if it was referenced in the ring.
Your question does not make clear whether Exchange1 or Exchange2 know about your real world identity. If they do, you've already lost your privacy. If they don't, depending on the scenario then perhaps it wouldn't even matter if you'd used a cryptocurrency without ring signatures at all. What good is it to see funds move on the blockchain, if neither the source nor the destination know your identity?