Context : The self-enrichment scenario for globular clusters ( GC ) requires large amounts of residual gas after the initial formation of the first stellar generation . Recently , Krause et al . ( 2012 ) found that supernovae may not be able to expel that gas , as required to explain their present day gas-free state , and suggested that a sudden accretion on to the dark remnants , at a stage when type II supernovae have ceased , may plausibly lead to fast gas expulsion . Aims : Here , we explore the consequences of these results for the self-enrichment scenario via fast rotating massive stars ( FRMS ) . Methods : We analyse the interaction of FRMS with the intra-cluster medium ( ICM ) , in particular where , when and how the second generation of stars may form . From the results , we develop a timeline of the first \approx 40 Myr of GC evolution . Results : The results of Paper I imply three phases during which the ICM is in a fundamentally different state , namely the wind bubble phase ( lasting 3.5 to 8.8 Myr ) , the supernova phase ( lasting 26.2 to 31.5 Myr ) , and the dark remnant accretion phase ( lasting 0.1 to 4 Myr ) : ( i ) Quickly after the first generation massive stars have formed , stellar wind bubbles compress the ICM into thin filaments . No stars may form in the normal way during this phase , due to the high Lyman-Werner flux density . If the first generation massive stars have however equatorial ejections , as we proposed in the FRMS scenario , accretion may resume in the shadow of the equatorial ejecta . The second generation stars may then form due to gravitational instability in these discs that are fed by both the FRMS ejecta and pristine gas . ( ii ) In the supernova phase the ICM develops strong turbulence , with characteristic velocities below the escape velocity . The gas does not accrete neither on to the stars nor on to the dark remnants in this phase due to the high gas velocities . The strong mass loss associated with the transformation of the FRMS into dark remnants then leads to the removal of the second generation stars from the immediate vicinity of the dark remnants . ( iii ) When the supernovae have ceased , turbulence decays quickly , and the gas can once more accrete , now on to the dark remnants . As discussed in Paper I this may release sufficient energy to unbind the gas , and may happen fast enough so that a large fraction of less tightly bound first generation stars are lost . Conclusions : The detailed study of the FRMS scenario for the self-enrichment of GCs reveals the important role of the physics of the ICM in our understanding of the formation and early evolution of GCs . Depending on the level of mass segregation , this sets constraints on the orbital properties of the stars , in particular high orbital eccentricities , which should have implications on the GC formation scenario .