You have to look at more then contracts and numbers to get some advanced knowledge.
The CFL provides TSN with content ~22 weeks of the year. The NHL provides TSN with games from October until May, which is a lot more games. The NHL is worth a half hour every weekday on TSN (That's Hockey) even in the summer. The NHL gives TSN the draft, and they also get a big show out of trade day. OTR in the winter is pretty much all hockey, all the time (and doesn't run for half the summer).
Oh, and the NHL attracts bigger sponsors willing to pay more. You see the beer companies tripping over themselves to sponsor the CFL on TSN the way they do Hockey Night in Canada (for that matter, Molson Canadian Leafs Hockey on TSN)?
That's the reality of the situation. Air Canada, Molson, Labatt, and a whole slew of car companies are willing to spend top dollar for national NHL advertising time. They're not willing to do that to the same degree with the CFL. Until that changes, the CFL won't get NHL money.
And even if you discount all that, the idea that the contract is going to more then triple without more competition then previously existed showing up is ludicrous. Stuff doesn't work that way in the real world. CBC's fee for Hockey Night in Canada almost doubled last time around because they feared CTV/TSN was going to nab the whole thing and it's CBC's cash cow so they couldn't afford to lose it. The same pressure doesn't exist on TSN for the CFL.