Generally speaking, it was equipped by garrisons of naval landing forces. I think, “offensive” unit like paratroopers or landing troops of NLF often used rifles or carbines.
Type Su Automatic Pistol (ス式自動拳銃, Steyr-Solothurn S1-100)
used by garrisons of Hainan island
original post (twitter)
Type Be Automatic Pistol (ベ式自動拳銃, SIG-Bergmann M1920)
Demonstration of weapons of Shanghai SNLF, a garrison of Japanese territories in the Shanghai settlement
Also, such submachine guns were equipped by some warships in Chinese coast.
According to this document by Japanese navy in 1933, (官房第５５６４号 ８．１２．２０ 軍艦出雲及鎮海防備隊に定数外消耗兵器供給並に兵器貸与の件に関する件), HIJMS Izumo had 4x Vickers 12.7mm MG, 4x Vickers 7.7mm LMG, 12x Type Su SMG and 2x Yamanouchi Short 5-cm cannon.
They equipped such ground weapon because at the warfare they organize naval landing force to support ground force. Actually, during Battle of Shanghai, she organized Izumo NLF to reinforce Shanghai SNLF.