John,
The tithe applotment records list families with land. In 1829 there were 3 Chambers families farming in the parish of Magherafelt. 2 different Davids and a Matthew, in Ballyheifer, Aghagaskin & Magherafelt town.
http://www.irishgenealogyhub.com/derry/tithe-applotments/magherafelt-parish.php
If your family were not listed in the tithes then that normally suggests they were labourers or in some other trade where they did not have any land. Farm labourers were very common and made up a large proportion of those who emigrated.
The family may have left because of the famine (a couple of million did) but there were other factors at play too. There had been a population explosion and there just wasn’t the land or jobs for that many people. The population in 1741 was 3 million. In 1841 it was 8 million (it’s only 6 million today). There was no spare land, Ireland had very few natural resources (no coal, oil, minerals) and so the industrial revolution largely passed it by, in contrast to Scotland, England, North America etc where hundreds of thousands of new jobs existed in coal mining, railways, steel making, ship building and so on. So people had been pouring out of Ireland all through the 1800s. All the famine did was speed it up a bit. In addition, increased mechanisation on farms and new farming practices reduced the need for farm labourers, plus mechanisation of the weaving industry made hand loom weaving (which many labourers did in the winter) uneconomic. All of these were factors in the decision to emigrate.
Your assumption that the family is descended from settlers, probably from Scotland, is very reasonable, especially if they were Presbyterians. (The Scots brought Presbyterianism to Ireland). Half the population of Magherafelt and Co. Derry/Londonderry has the same origins, arriving in the 1600s. Some came as part of the Plantation 1610 - 1625, some remained behind after the Scots army was disbanded at Carrickfergus at the end of the 1641 uprising, and there was a large surge of settlers from Scotland in the 1690s due to famine there.
This link takes you to Maitland’s history of Magherafelt written in 1916. You may find it helpful:
https://archive.org/stream/historyofmaghera00mait/historyofmaghera00mait_djvu.txt
Description of the effect of the famine in Magherafelt (source is PRONI & in turn Bill Macafee’s website).
http://www.billmacafee.com/otherrecords/faminebackground.pdf
The church records for Magherafelt are generally not on-line and so if you want to research them you need to get someone to go to PRONI. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net