If the tmux shortcuts don't work you need to start by typing the commands mannually.
tmux split-window and see if those work.
If they do, you need to check on the mannual pages
man tmux and see if
tmux new-window and all other command's shortcut you are trying to use are bound as you think they are in section KEY BINDINGS.
In the KEY BINDINGS section look for the prefix key and other shortcuts which you are trying to accomplish if they are defined with the keys you are pressing.
Not really sure about Ubuntu repositories but it's better if you install the latest version of tmux from their github repo yes means building from source.
After a quick search i found out that version: 2.2 of
tmux that ships with
ubuntu 16.04 is buggy so i think you should update from source to latest as they suggest.
tmux -V (for version) matters sometimes so updating to the latest can prevent most problems.