I believe imo.IM's Steam functionality is based off SteamRE, which is a project to reverse engineer the Steam protocol. Since the Steam protocol is not something that is made available to third parties it's likely that this connection is established as though a second Steam client has just logged into the service, which will log you out.
It's worth noting that such third party "solutions" are not officially supported by Valve or Steam.
If you wish to use Steam on your mobile device you should stick with the official Steam for mobiles application, which will allow you to stay signed in on your home computer while logged in on your mobile device.
Something important you should consider
Using a third party application to access Steam is technically against the terms of service you agreed to when you signed up and created your Steam account, and may get you banned.
Quoted from section G (ii):
host or provide matchmaking services for the Software or emulate or redirect the communication protocols used by Valve in any network feature of the Software, through protocol emulation, tunneling, modifying or adding components to the Software, use of a utility program or any other techniques now known or hereafter developed, for any purpose including, but not limited to network play over the Internet, network play utilizing commercial or non-commercial gaming networks or as part of content aggregation networks, websites or services, without the prior written consent of Valve;