Zam was really mean to Logan when I first introduced him, it went beyond what you are describing, so I started using Feliway.

She went from hurting him to the occasional growl and hiss. Now they cuddle.

Although, lately they have been getting on each others nerves. Chasing each other and swatting and making not so nice noises.

I think it's a 'Spring Fever' thing.

Don't worry! They'll be buddies in no time.