The extra money is not from BT.
Domestic and Overseas TV deals are negotiated in 3 year stretches, and both run concurrently.
Overseas TV money is shared out equally between all clubs. Last year it was £18m, paid monthly. It's increased this year.
Domestic TV money (Sky, BT, BBC, various online distributors) is split:
25% "membership" pot. This is split equally between all clubs. This is paid in two installments - August and January.
25% "facility fee". Payment for each live match shown in UK. Guaranteed minimum 10 appearances. Last season was £575k / match. Not sure for this new deal. This is paid quarterly (I think).
50% "prize pot". Bottom club gets X, 2nd bottom 2X, top team gets 20X. Last season was about £800k / place. Not sure for the new deal. This is paid at the end of the season.
There's also money set aside for parachute payments and a "solidarity" payment to the Football League.
There are 7 packages of live games that are sold, of 13 and 26 games. BT bought 2 packages, including one that gives them first dibs on games for that round. They're paying around £7.8m per match. Sky are paying around £7.15m.
So the key to Everton's finances are the schedule of payments. If we finished 6th again, we could reasonably expect to earn around £35m more in broadcast revenue than last season. Everton are far too dependent on broadcast revenue as a proportion of total turnover as matchday revenue is limited by the stadium (corporate hospitality) and our commercial income is, to use a technical term, gash.
Y'all better hope that BT stay the course, cos if Sky ever have to bid againt the likes of ESPN (cheapskates) only then the value of the deal will drop hugely and we'll be screwed!