It shows up automatically in Lr only when in Photoshop you do a <save>, as opposed to <save as>.
In order to create a JPG in Photosop you have to do a <save as>, so it doesn't show up automatically in Lr.
When you do a <save as> Photoshop creates a new file which Lr "knows" nothing about. So, no automatic showing.
A better workflow would be: In Photoshop just <save> your TIFF.
If you need a JPG, create it with Lr by exporting your TIFF in a JPG format and check the box <Add to this catalog> in the Export Dialog.
Your JPG will then automatically show in Lr.