Is having AES tables on a distinct physical page enough to avoid cache timing attacks?
No

You are misunderstanding how such attacks work. It's not that your page gets shared to some attacker process. Attacker might not even be present on your computer, only measuring time over internet.
Such attacks only depend on fact that if you access index 5, then every next access to index 5 will be faster. It doesn't require any method to remove data from cache (it will go away on it's own), but those can make attack faster.

For example here is attack that only used a server that included a cycle-exact time. No attacker program was present on victim machine.

As a side note: When process is attacker running as a normal-privileged process, it has access to all other normal-privileged processes in many OSes (for example Windows), so attacker can simply read key.