That's all correct that players are paid on a daily basis bi-weekly. If the Bruins were under the cap, then yes sending down Bjork for a few days would create additional cap space (technical term is Payroll Room).
The problem here is that according to CF the Bruins are over the cap even without Bjork. If you look at the daily cap tracker chart CF shows that Boston has been over the cap (ACSL) every single day of the regular season. That means at this point in time Boston has accumulated $0 Payroll Room. When teams are over the cap/ACSL using LTIR then the unused LTIR space does not accumulate. So it doesn't make a cap difference if Boston is using $1.505m of LTIR space now with Bjork vs. only $580k of LTIR space while he was down the past few days.
I looked for other reasons why it might be advantageous to use emergency recall for Bjork rather then a regular recall but I'm still failing to find a reason why. I sent a question to CF, hopefully they'll be able to explain it.
Hopefully CF can give the definitive answer, but I think this is how the Bruins got burned a couple years ago when Chia signed Iginla to that bonus contract when they still had Savard on LTIR.
Towards the cap, salary counts first, then you can exceed the cap by LTIR, then you can exceed even further by bonuses (ELC and 35+ contracts). This issue is only because the cap requires LTIR to be applied first before bonuses, not after bonuses.
With Bjork, he has ~$300k bonus potential including ~$100k guaranteed via signing bonus. For easy math, lets say 200 games in season so his bonus earnings could be $1.5k/day for every day he's on the roster. Because bonus apply after LTIR, Bruins were exceeding the cap beyond LTIR by $500-$1.5k every day he's on the roster while they are over the cap--the final numbers won't be known until the end of the season to see if he hit the performance numbers but the signing is guaranteed money they need to account for. When guys come off LTIR, even if they get down to exactly the cap with all bonuses going forward, they still have to account for the bonuses for all the days earlier in the season when they exceeded the cap. That includes DeBrusk and Kuhlman's bonuses too. Otherwise this rolls forward to become a cap hit next year. One less day over by $1.5k means one less day they need to be under by $1.5k in the future.