A Comprehensive Grammar of the English Language (Quirk et al) explains:
The basic reflexive pronoun is sometimes optional, in the sense that
it may acceptably be replaced by the more usual 'ordinary' objective
pronoun. The self-forms are chosen to supply special emphasis. [The
scare quotes are mine, EA, and I'd say the reflexive forms are
sometimes chosen for formality rather than emphasis]:
(a) In some spatial prepositional phrases:
- She's building a wall of Russian books about her(self).
- Holding her new yellow bathrobe about her(self) with both arms, she walked up to him.
- Mason stepped back, gently closing the door behind him(self), and walked down the corridor.
- They left the apartment, pulling the spring lock shut behind them(selves).
With 'He felt anger rising inside him', a metaphorical (container ... level) spatial usage, licensing 'him', 'himself' could certainly be chosen instead. However, it would sound perhaps a little ponderous, even stuffy, rather than punchy. In fact, punchier still would be 'He felt his anger rising.'