Hi Joan
Your Grandfather was born in Liverpool, it was your Gt Grandfather who was born In Douglas, Isle of Man. Your Gt Grandfather more than likely moved to Liverpool for their work, as did many. (My Grandfather did).
Looks like Jane Jones may have been your Grandfathers maternal Grandmother, Mary Davies nee Jones being her sister? (Mary Jones married Morris Davies 1855 Liverpool). Maybe both your Gt Grandparents had passed away by 1901 - although I couldnt find any death for a Joseph John Shimmin on FreeBMD .
Looks like your Grandfathers paternal Grandparents - your GtGt Grandparents, were Thomas and Jane Shimmin nee Hudg(e)on and on 1881 Census they were living at 21 South Quay Braddan, Thomas aged 49 born Braddan, Ropemaker, Jane aged 45 born Rushen and children Thomas 24, Cabinet Maker, Gilbert Smith aged 13 and Isabella Jane aged 7 (all born Douglas). Possible burials for Thomas and Jane on www.iomfhs.im
SHIMMIN, Thomas 66 Bra 21 Aug 1897
SHIMMIN, Jane 63 Bra 11 May 1898

You will need to confirm this by obtaining birth/marriage certificate for your Grandfather and marriage certificate for your Gt grandfather.

Hope this helps.