Apple TV - choice of the account to sign in

Correct. Home hubs for each defined home must all be registered with the same Apple ID account. If his Apple TV box is registered with a different Apple ID, then it can’t be a hub for that same connected home for HomeKit. Maybe that is no issue at all, depending on HomeKit accessories that can or cannot connect to any other hub.

Apple TV’s account screen allows for separate sign-ins for the Store (and Family Sharing), and for iCloud. You can set a different account there, so that the iCloud services match yours, and then this unit is included as hub for HomeKit. Depending on iCloud services that he wishes to use (maybe none) through that device, that may or may not be a loss. That is the choice that you two have to make.

See: Set up your HomePod, HomePod mini, Apple TV, or iPad as a home hub - Apple Support

There can be multiple home hubs, and that will likely be beneficial. One hub will be automatically designated as ‘connected’ while the others are in ‘standby’ mode. They all still contribute continuously, so don’t worry about which one is said to be connected.

All HomeKit home hubs need to be registered with the same Apple ID account for iCloud services. E.g. the current models Apple TV can have multiple accounts, but the account setting for iCloud services should match, for HomeKit home hub use.

With Family Sharing, each group member can (and should) access the shared services on their own account. He should sign in with his account. Then he’ll have his own queue list, watch history, and recommendations.