Please tell me, if I understand your topology correctly:
Linksys router < - WiFi - > RUT360 < - WiFi - > Mobile phone
Where RUT360 basically acts as a WiFi extender and the configuration you have attempted is as shown in this video. Is that the case?
The first thing to check is whether Linksys and RUT360 are on different subnets.
However, considering that wired connection works (I assume LAN port of Linksys is connected to RUT360 WAN port), I suggest to make sure that the wireless key used is correct.
If none of the above resolves your issue, I would like you to attach a troubleshoot file to your question. Please, replicate the issue by first attempting to connect RUT360 to your Linksys router, then access router's WebUI, go to System -> Administration -> Troubleshoot section and download troubleshoot file from there. The logs in the file might provide more insight into the issue.