Carry On-v1.1.1
Forge v1.10.2-2316

I noticed that most modded chests or tile entities don't rotate when placed to face the direction the player is facing, such as the Iron Chest Mod or the Bibliocraft Mod.

For most TEs (even modded) it works fine, but these two do not use the provided Minecraft rotation mechanics (I can't tell you why).

Yep, exactly. So this will unfortunately not be fixed.