With about a thousand hours instructing on them, I've done many hundreds of spins on about twenty different airframes. I never had any uncomfortable moments and although different airframes exhibited slightly different characteristics, the recommended entry and recovery technique leads to safe spin training.
However, there are different ways to enter a spin and this leads to different characteristics. The recommended entry is to apply full rudder at 50 knots and soon after full back stick with the ailerons neutral. It's unlikely that an inadvertant spin will have such an enrty - a more plausible entry would while in buffet, induce wing drop with rudder and attempt to correct with out spin aileron. This will very likely induce a spin and this spin is very different to the intentional. The former is a stable non-oscillatory manouvre which settles into the fully developed stage at about a full turn with about 50 degrees nose down, recovery taking about two turns. The latter is a flatter, slower rotating spin with oscillations and which enters the fully developed stage in about half a turn or less. Rudder is noticeably less effective and the recovery takes about three to four turns.
There are few records remaining as to the accidents which led to the fitting of the anti spin strakes, but it's clear they are result of a number of accidents occurring to the RAF aircraft soon after entry into service. De Havilland came up with the modification and it's not dissimilar to the one fitted to the DH82 Tiger Moth. About the same time, the wide chord rudder was fitted and this was intended to give better rudder authority during aerobatics, especilly slow rolls. But not for spin recovery, and in fact contemporary documents mention that the wide chord rudder does not aid spin recovery.
And the term anti spin strakes is a bit of a misnomer. We referred to them as such in the RAF, and the CAA's CAP562 leaflet 11-1 (Chipmunk Spinning and Aerobatics) also refers to them this way. But a 1960 DH document simply refers to them as 'Fuselage Strakes' and I suspect the wrong nomenclature has stuck with time. CAP562 describes them as increasing the aerodynamnic drag of the tail, damping rotation in yaw and steepening the spin. This doesn't really make sense if you think about it and differs from the RAF's explaination of how they work which is that at the high angle of attack of the spin, they act as a vortex generator and re-energise the airflow over the rudder making it more effective. This would help recovery in the latter type of spin I described, so I'm sure they were fitted in response to inadvertantly entered flatter spins which recovery from which would quite clearly benefit from an increase in rudder effectiveness.
An Australian document written in 1960 after flight testing of Chipmunks in response to series of accidents mentions that;
"It was found that although the strakes had no effect on the entry, the spin itself or on the recovery of an aircraft with good recovery characteristics, they did tend to shorten the recovery time slightly on an aircraft normally slow to recover, but it was only a reduction in the order of three quarters of a turn in the worst case"
The UK CAA don't agree, and UK registered Chipmunks without fuselage strakes and the wide chord rudder are prohibited from aerobatics and spinning.