Watch for bullet noses that would put pressure on the primer: cartridges in a tube magazine tend to "bounce" under recoil. If the nose on the FMJ is blunt and the flat is larger than the diameter of a primer, it should not put pressure on the primer under recoil. I have a box of FMJ 357 Mag, but the flat nose of the bullet is much larger than the primer pocket. I checked and I have fired all my FMJ 130gr 38 Spl (BTW that is the same style as the USAF issue ammo for the .38 revolvers issued to pilots) so I can't say if I would use it in a tube magazine.
I have a Rossi Puma 1892 clone and a Ruger Security Six and I simply make a point of buying jacketed bullets with exposed lead , hollowpoint or flatpoint noses, in either .38 Spl or .357. Quite frankly, the FMJ was bought by accident, but I would not expect it to cause a detonation in a tube magazine. I suspect the noses were flat due to factory concerns about use in tube magazines.