Well I researched and this is what needs to be done with your GMAIL app:
Change notification settings for certain labels
Open the Gmail app Gmail.
In the top left, tap Menu Menu.
Tap Settings.
Select your account.
Tap Manage Labels.
Tap one of your labels, like Important.
Tap Sync messages and then Last 30 days or All. If you don't sync messages, you can't turn on notifications for that label.
Choose your notification settings for that label. Repeat this for any labels you want to get notifications for.
Maybe check this out to see what gives