Trip from A to C with a change of train and TOC at B.
A to B train delayed. This would have caused the B to C connection to be missed and thus generated about an hours delay.
However B to C train also late so connection made. Upshot is arrived at destination late.
Which TOC is responsible for paying me?
By the book, the 'fault' lies with the first TOC that delay you, and as such you claim to the TOC for A-B.
More specifically, it's the first delay that would cause the itinerary you are travelling on to become impossible - in this case, A-B is delayed enough that the minimum connection time at B for the service B-C is fouled, then the itinerary can't be adhered to, and 'fault' is with TOC #1. It is The itinerary is provided before travel and does not react or adapt to delays. The delay on service B-C should be immaterial, as if B-C was running to time, then according to the itinerary you would have not met the minimum connection and had to catch a later service. TOC #1 couldn't refute this and should approve Delay Repay.
It sounds like someone at TOC #1 has reviewed the Delay Repay claim and either doesn't know how it works, or is trying to bend the rules to avoid a payout:
It seems that they're arguing that the delayed departure of B-C was long enough after A-B arrived at B, that it theoretically satisfied the minimum connection time at B, and due to this, their initial delay was immaterial because you still caught the service B-C as specified on your itinerary: the delay A-B didn't affect your actual arrival time, so TOC #2 should pay out, and only for the delay on that segment.
This logic is incorrect (itineraries are static, they don't adapt to delays), and I suspect that TOC #2 would refuse to pay and say it's not their problem as TOC #1's delay preceded theirs. TOC #2 should not pay out for this, and if they did you'd get less than you were entitled to.
Unfortunately the fact that TOC #1 are passing the buck is a tacit admission that they did in fact delay you IMO, as if they reject your claim in any way then they're trying to tell you they didn't delay you despite the fact their service didn't run to time

.
It's the first TOC's problem, if they keep rejecting it just keep appealing, get a deadlock letter and go to the Ombudsman.