They believed in their chief; he was rarely wrong, rarely sent them down the wrong path. When he did, it usually no more than a simple mistake with no harm done.
While they may not have the bond and undying loyalty of the Shinsengumi, they had a deep respect for their commander's experience and wisdom. If he said to jump, that would ask how high without a moment's hesitation.
So they didn't question this either.
Some did find it odd that he suddenly had an ashtray in his office; he didn't enjoy smoking and discouraged it in his officers. Weirder yet was the odd smell and brand of the cigarettes they saw crumbled in that ashtray. Who thought Mayoboro cigarettes were tolerable?
Then there was his new frequent visitor. Most days, he'd stomp into their headquarters without invitation or warning and head right into the chief's office.
A majority of the time, he was yelling about the number of text messages he'd been getting, how they're interrupting his work and his sleep, and so on. But eventually, the noise would die down. He'd leave some time after that looking somehow guilty.
It was odd for the Shinsengumi vice chief to visit so often that he could walk right through this security, but they didn't question their chief's orders.
When they saw them on a shared day off, walking close enough for their shoulders to occasionally brush, they thought it was odd. They were puzzled by the hint of red in Hijikata's ears and how their bickering seemed so much friendlier.
It was odd, but their commander always knew best...and it was nice to see a smile on Isaburo's face now and then.