Changing the coordinates of an entity is visually smoothed by a 3 tick delay. For this reason, if just after teleportation, an armor stand with the NoGravity or Marker tag is rotated, e.g. with the tp facing command, it stops visually and after a while moves to its expected position.

Commands used in the attached video:

command block 1: summon minecraft:armor_stand -6 4 9 {NoGravity:1}
command block 2: tp @e[type=minecraft:armor_stand] -6 5 12
repeater (1 redstone tick = 2 command ticks)
command block 3: execute as @e[type=minecraft:armor_stand] at @s run tp @s ~ ~ ~ facing entity @p