First, the terminal double bond reduction. Then, the classical ozonolysis, and rearrangement to 5-membered cyclic peroxide. Then the O-O bond heterolytically breaks up, so that O+ is on the carbon next to carbonyl. The O- attacks the carbonyl to form a 6-membered cycle. Then, electron pair migrates from O- to form C=O bond, C-C bond goes on O+. We have got then an aldehyde acetate-lactone. NaBH4 hydrolises it and transforms the aldehyde to the alcohol, finally lactone closes spontaneously.
Ozonolysis of enones is complicated and generally results in additional cleavage of the carbonyl-alkene sigma bond. A simplified mechanism only giving a single rearrangement to the bicyclic trioxolane is given below.
The exact mechanism is significantly complicated, and varies with the temperature and the number of equivalents of ozone absorbed. Both carbonyl oxide intermediates can form and can recombine intermolecularly to give a tetroxane which also decomposes to the anhydride.
For an in depth mechanism of ozonolysis of a related compound, verbenone see the following: