HDMI and controller issue

I’m facing a possible issue.
Currently I’ve chromecast ultra and ps4 linked to the projector via an HDMI splitter. And when I start the projector it goes to hdmi source, which is fine, but could there be a choice to set a default to start with.
So the issue, pressing the home button doesn’t take it to home, does nothing. I’ve to disconnect the HDMI and reconnect, and then the home button press is the followed.
Any thoughts?

Yes, it happened to mine too but sometimes it works when pressing home button. Maybe some bugs.