A CONUNDRUM

I am currently seeking advice about seemingly conflicting information on James Carey.

The Carey family I found in the 1881 Quebec census was the only one with a son James that fit his age, name, place of birth and location.  I found James in the U.S. federal censuses from 1900 on forward.  His immigration dates per the censuses varied from 1887 to 1890.   The only slightly odd thing was one census showing he'd immigrated 1887 while his daughter immigrated 1888.

A very nice woman with a Quebec genealogy website located the marriage of James' parents, John Carey and Mary Powell.  The surname Powell fit as a James Powell lived with the family at the 1881 census.

I then located a marriage record for James and his wife Eliner Rheaume - which also named their parents.  James' parents were John Carey and Mary Ann Powell.

Then I started looking for the family in other censuses.  And found the 1891 census listed James twice - in Quebec.  Once in his own household with Eliner and their 2 children.  And once in his parents' home, without Eliner and the children, marital status "married".

So how could James be in the U.S. by 1890, and in Quebec in 1891?

I've done a little reading online about Quebec emigration to New Hampshire.  Turns out, similar to my Norwegian ancestors, French Canadians might emigrate to the U.S. to make some money and return home - or at least visit a time or two.  Could James have been visiting in 1891?  Or, are the federal censuses [all 3 or 4 of them] entirely wrong about his having immigrated by 1890?

Offhand, I don't know a way to check immigration records between the U.S. and Canada.  I also wondered about James Carey's naturalization records, which might provide an immigration date, but I don't even know if he moved from Quebec directly to New Hampshire, or if he perhaps lived in Maine or Vermont first and was naturalized in one of those states.  

Hmmm...