Cross tie feeder is normally closed, isn't?

As I don't know the voltage level, I can't say for sure anything. But on distribution level we don't use interlocks. For generation plants we use a timer, and automatic open the tie if the timer is exceeded.
Sort of depends on your application, and other details.

The two switchgears have two dedicated incomers each. Hence, the cross-tie is closed only when required (and normally open) I guess.
In such a case, it is always recommended to keep the CB of the tie feeder closed on one side, with the other side (CB) left open. This is to ensure that the tie feeder is live / healthy.
The protection relays may be given a second group of settings (assuming numerical type protection relays) that are sensitive to isolate the feeder in case it develops a fault when live but not connected at one end. The protection group switching can be automatic based on the CB/DS status.
Connecting the cross-tie at both ends should only be permitted when one of the main incomers + Bus secion breaker is open or when both the main incomers are open with bus section closed. This is to ensure that the fault levels at either of the switchgear are not exceeded beyond permissible levels.
Trust the above helps.

It goes like this:

Switchgear A feeds switchgear B through cross tie CB(A) during normal operations.
Switchgear B only supplies switchgear A through cross tie CB (B) if the power flow to switchgear A (both sources) fails.