Also, it appears that Fisher was as sept of Clan Campbell.
Please don't get hung up on clans. All this 'if your surname is xxx you belong to Clan yyy' was dreamed up by the Brigadoon industry in the 19th and 20th centuries.
Fisher is an occupational name. It derives ultimately from Old English, and occurs as Fischer in German, Pecheur in French and so on. A moment's thought will tell you that it must have evolved as a surname all over Britain, and therefore not all Fishers are connected to any clan, Campbell or otherwise.
Don't forget that many fishermen would have fished on inland lochs and rivers, not only in the sea. So it isn't especially odd that there were Fishers in the lands of Clan Campbell.
From G F Black's
The Surnames of Scotland, the surname first appears in Perth in 1292, 1338 and 1344, in Atholl in 1455, Lanark in 1488, Carstairs in 1513, and Edinburgh in 1603.
He also says that in Perthshire the name is used as an Englishing of MacInesker, from Gaelic Mac an Iasgair, which means 'son of the fisherman'. This surname occurs from 1494 in Perthshire, Argyll and Aberdeenshire.
Out of sheer curiosity, I looked at the distribution of baptisms of Fisher and phonetically similar names by county from the earlest records until 1750.
The largest number in any county was Perthshire with 561 occurrences
Then Lanarkshire 309
Midlothian 304
Ayr 141
Angus 125
Stirling 97
Argyll 88
Roxburgh 76
Fife 71
West Lothian 41
Dunbarton 40
Kinross and Kincardine 24 each
Renfrew 23
Dumfries 18
Clackmannan 14
Peebles 13
Kirkcudbright 10
Berwick 8
Selkirk 4
Moray and Banff 3 each
Aberdeen, Orkney and East Lothian 2 each
There were none in Bute, Caithness, Inverness, Nairn, Ross and Cromarty, Shetland, Sutherland or Wigtown
Of course this is a very crude analysis, because it takes no account of the total size of the population of each county. Nor does it allow for the many gaps in the surviving records at that time.
So while it's fine to note where there might have been clusters of Fishers in the early 18th century, you're on very shaky ground if you extrapolate to say that because that's where the largest clusters of Fishers were, that's where your Timothy's parents must have come from.
Interestingly, Timothy is a very uncommon given name in Scotland. He occurs only 43 times in the surviving Scottish church records before 1750 (compared with, for example, 40,880 occurrences of John).
As for anything else happening around that time, it was soon after Culloden, but also at the start of the Highland Clearances.
And as for his wife's religion, if his family were fleeing after Culloden, they might have been Episcopalian or Roman Catholic, but if they were among the early clearances, they could also have been Presbyterian. I doubt if the fact that she was Puritan would be very helpful in tracing his antecedents.