Does NRZ-I have a synchronization problem?
For example, if a sender sends 1111 and the receiver's clock is twice as fast as the sender's clock, the receiver will interpret the pattern as 101010.
Isn't that a synchronization problem?

Not in this context, no.  When you design a synchronous communications link like this you assume that the uncorrected receiver clock is pretty close to the transmitter clock.  &quot;Pretty close&quot; can vary (and you design the communications protocol with an allowable mismatch in mind), but \$\pm 10\%\$ is easy to achieve with RC circuits, and \$0.1\%\$ is easy with crystal-controlled circuits.
Part of a system designer's task would be to assess the tradeoff between protocols that allow quicker synchronization at the expense of a closer initial match between receiver and transmitter (and hence more expensive receivers and transmitters) vs. the opposite.