Remember that as long as a static magnetic field is present (even the earth's magnetic field), nuclear spins are always precessing. This remains true even after they have been subjected to RF-pulses. An RF-pulse of any value will change the orientation of magnetic moments for all the spins in the sample, but the spins will continue to precess.
The source of confusion likely comes from the fact that we often talk about the net magnetization (M) before and after a 180°-pulse. If M starts out in equilibrium, perfectly aligned with Bo, it does not precess (though the individual spins that compose M are continuously precessing). This is similar to a gyroscope or top that does not precess when directly vertical. If this perfectly aligned M is now perfectly inverted by a 180°-RF pulse, the inverted M likewise will not precess (though the individual spins that compose M continue to precess).
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This question reminds us that not only M, but individual proton spins are always precessing around Bo regardless of their "orientation" in space. Nearly all spins are in a linear combination of spin-up and spin-down states with respect to the main magnetic field and will precess at various angles around the z-direction. A very small number of spins will be in pure spin-up or spin-down states, and their angular momentum will therefore be oriented exactly parallel or antiparallel to Bo. Spins in these so-called stationary energy eigenstates will remain in these states and not physically precess, though their wavefunctions will accumulate a complex phase factor.
Elster AD, Burdette JH. Questions and Answers in MRI, 2nd Ed. St. Louis: Mosby, 2001, pp. 22-24.
Levitt MH. Spin Dynamics. Basics of Nuclear Magnetic Resonance, 2nd Ed. Chichester, UK: 2012, pp 231-258.
Is precession the same as resonance?
How does B1 tip the net magnetization (M)?
What is net magnetization and how does it apply to NMR?