Sorry for bad explanation.
When somebody joined the crew and serve captain , his loyalty belong the his captain.
Jimbei made agreement with big mom with his will. he choose yonkou that protect ısland. nobody force to choose Big Mom.
Then , he decided himself to abondon bigmom and join the SH.
When he wanted to seperate first time , he scared death and keep staying the Big Mom Crew.
And then still he was at Big Mom , he helped Luffy and Nami to save .
And he clashed Big Mom and her army.
Then , when there was at chaos , jimbei said to BM ı am leaving crew. And against big mom df , nothing happened (most bullshit moment which means BM DF trash.)
and everybdy said that jimbei is noble.
But Big Mom is one of the big captain that has her ambition and she manage crew according to the her style.
Jimbei betrayed Bigmom for me.
Let say it is not like that.
When sanji did same thing , we know what everybody said about sanji.
Just ridicilious.