Hi Rendy,
Performance in shared hosting is usually unpredictable, your another site could be running on different machine unaffected by this (a hosting could have many different servers and a server could have multiple sites sharing together). I’m not saying it’s the case, but it usually happens.
As for browser performance report, I’m not sure what you’re referring. The only information displayed on browsers are loading speed of site resources, it doesn’t display any information of server internal processing. If it does, then I could easily point it out without any help from the hosting and I would gladly do it 
Still, I’ll continue checking but as of now, I can’t find anything since it’s a shared hosting. As it only displays the access logs and traffic stat in CPanel.
Thanks!