For most products, performance requirements are subsumed by usability requirements.
With most products, users want to achieve functional goals within a certain amount of time. The amount of time it takes to achieve a functional goal is typically one measure of usability. Finer-grained response times can also impact usability, however. If a user clicks a button and nothing happens for ten seconds, the user may get frustrated and will almost certainly wonder what is happening.
So your product manager shouldn't necessarily include performance requirements per se, but should almost certainly include a full suite of usability requirements that include performance metrics.
The exceptions are those products that don't have much of a user interface component. Some products deliver functionality by themselves, largely without user intervention or interaction. The speed with which they deliver such functionality is a matter of performance but not usability.