Typically this behavior is tied to the way the messages are being forwarded or the provider you are using. You are more likely than not to receive SPAM on the aliases in question so really what you want to do it is get Gmail not to automatically assume the forwarded emails are SPAM but rather behave as it typically does and use other factors to determine the SPAM score.
Usually, the best way to use a 3rd party email account such as cPanel or such with Gmail as your front-end is not to forward the mail but rather have Gmail reach out via POP and remove the mail from the other account. This allows you to enjoy the BENEFIT of Gmail's SPAM filtering and other features you wish to use without the behaviors you are currently experiencing.
You should setup 'Check mail from other accounts' under settings and also 'Send mail as' and 'Reply from the same address the message was sent to'. All these settings can be found on the accounts tab of Gmail settings (https://mail.google.com/mail/u/0/#settings/accounts).
If for some reason this isn't acceptable to you, Dynu, has full-featured email for $19.99/yr that I use only as a catchal forwarding to my Gmail account and I don't have the problem I normally encounter with the massive resellers and I do the same as you: https://www.dynu.com/Email/FullService
I would say if you already have everything setup at a host, the POP solution is ideal as it leverages everything you already have in place just in a different way, and you are likely better off archiving your email at Gmail than in the mailbox at your host.
Hope that is clear.