and why the runners agree to re-meet instead of just sending it via matrix?
That part's easy -- in the Matrix, the walls don't so much "have eyes" as "don't exist," and a good hacker can easily eavesdrop with no one the wiser. You *can* have secure Matrix communication, of course, but it takes some serious technological know-how, which Mr. J may not have. For this and other reasons, insisting on a face-to-face meet is pretty Standard Operating Procedure for Shadowruns, so there's not really a need to explain it.
Another interesting angle for the "Johnson is straight but the Yaks interfere" approach is that the players might assume or suspect that he's crooked, but then find that they're wrong. Which means that whenever it seems like they've been doublecrossed by a Johnson in the future, they'll always have at least a little doubt.
As for why the Yaks might want the Runners dead, there are any number of reasons that might be the case. Off the top of my head:
Mr. J is a liaison between Renraku and Yakuza Family A, and is sending the Runners on the current mission as a favor to Yakuza Family A. The mission is disguised as a standard Renraku op so Family A can keep their involvement in it a secret and the Runners won't know who they're really working for. Yakuza Family B, a rival to Family A, somehow finds out that this is occurring, and tries to intercept the paydata and kill off Mr. J to get an edge on Family A and damage their reputation with Renraku. The Runners are only targeted (a) because they happen to have the paydata, and (b) because they're loose ends who might be able to piece together what actually happened. Mr. J survives the assassination attempt, but has to go underground and out of contact with the Runners, leaving the Runners high and dry until they've realized what's happened and can track him down.
It's a pretty basic premise, but it should work just fine. If you want further inspiration, Shadowrun fiction pieces are full of stuff like that.
As for how the players find out what's going on, I like to "plan out" one or two methods by which they might get the info in case they get stuck. But otherwise, I like to just let them try and figure out how to do it. If the Yaks are handling the hit themselves, the fact that all the assailants are Asian or Asian-American (or whatever nationality) will probably be a pretty major tipoff, and if they get photographs of the attackers (or their corpses), they can pass them around to their contacts and see if any of them recognize them, or know anyone who might recognize them. Then, if the Runners are smart, they'll see if Mr. J had any dealings, friendly or otherwise, with any of the local Yakuza families. Once they realize that Mr. J regularly dealt with Family A, while all the attackers were from Family B, they should figure it out pretty quickly.
Of course, finding out any of these pieces of information might involve more than just asking their contacts for info. They could have to shake a street snitch down for information, or steal/hack the comm of a local Yak lieutenant.
Man, now I want to go write a Shadowrun.