There is no mutation caused because a word follows a vowel.
There is a difference between the mutations caused by ei (his) and ei (her) - this is explained in the notes for 'Possession' earlier in the course as well as for this section 'The News':
- ei (his) - soft mutation
- ei (her) - aspirate mutation, or h- before a vowel.
Other mutations or changes are caused by other possessive pronouns - see the notes.