I believe that Tahm's devour applies Stasis, same as Zhonya's hourglass, rendering the target invulnerable (all damage reduced to zero) and untargetable (can't be the target of new abilities).
Neither invulnerable nor untargetable removes tethers or DoTs (invlunerable prevents damage from DoTs while it lasts, but if invulnerablitiy expires while the DoT is present you will begin/resume receiving damage) nor does either invuln./untarg. prevent CC.
Untargetable does not remove tethers nor does it prevent CC.
My understanding (have not tested) would be that if tahm devours someone tethered by soul shackles, it would not break the tether. If devour ends before soul shackles then both the stun and damage would apply. If soul shackles duration finishes first, then the stun would still apply but the damage would be negated by invulnerability.
So Soul Shackles is unaffected by devour (apart from preventing the tether from ever forming in the first place on an already-devoured target).