How to extend browser-based VPN to other applications?

If I Google for "what's my IP" before and after I enable a VPN add-on (Zen-Mate) on my browser (chrome), I get two different IP addresses. I'll call these two addresses my base IP and VPN IP addresses, respectively.

When the VPN chrome add-on is enabled, the VPN IP address seems to work only for requests I make via chrome. Requests performed through other apps/tools (e.g. VLC or youtube-dl) produce the same results as when the VPN extension is disabled (IOW, they retrieve content different from what I get with chrome, or fail altogether).

My other experiences with VPN are very different. In those other cases, my machine behaves as though it belongs to the virtual network, and therefore all requests I make are treated by the responding servers as coming from the same in-network IP address, irrespective of the application I used to make the request with.

Is there some way I can configure my machine so that the VPN IP address I get when I enable my browser's VPN add-on applies to all the requests I make from my machine?

FWIW, my OS is Linux (Debian).

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