Messages in Gmail labels do not get pushed

I have a gmail account with several labels. I filter messages so they bypass the inbox and get filed under a specific label.
I am finding that such messages do not not automatically appear. In Thunderbird and my android phone I can subscribe a folder and get IMAP push for it so emails appear instantly. Not with eM. I can’t find where I can subscribe to a folder.
Unfiltered messages sync fine.

Another issue is that I don’t see a taskbar notification (Win 7) for new messages that go directly to a label/folder. It’s a problem because I use eM for business and this kind of automation is quite essential.

Hi Yury, eM Client only synchronizes the inbox folder in an established connection as well as showing notifications for Inbox only.
Although if a new mail is available in another folder there should be three dots displayed next to that folder.

You could enable “Download messages for offline use” in Tools > Accounts > Your account > IMAP tab, in order to have all emails downloaded, otherwise all other folders are synchronized after you open them (click on them).

Thank you for understanding,

Thanks for replying. I am afraid these are key issues for me and I would guess for many others in my organization. In a heavy business use you need email rules to be productive. Also, three dots is just not visible enough. New email is new email, regardless of which folder it went. Most clients are capable of that.
Oh well, I guess its back to Thunderbird for me.