People recommending deploying your safety sausage on a spool/reel are wrong and are giving dangerous advice.
In chorus...everyone together... "
or you're gonna die!"
This is a complex skill to execute safely in a stressful situation and requires training and practice.
Let's assume that all concerned, epsecially the OP, are aware of the need to learn and practice the skill...and that the equipment advice was given in this assumption
The consequences of getting it wrong can be very serious. I have witnessed one uncontrolled ascent when a diver became entangled and have heard of many more.
Yes, this does happen. However, it is far more likely when divers utilise the 'safety sausage' with attached 6m of loose line, than if they properly deployed a DSMB from with a finger reel from a deeper depth. The loose line that comes with cheap 'safety sausages' is IMHO much more dangerous.
It's actually pretty hard to get entangled using a finger reel. If anything goes wrong, the reel can be released and it will continue to unspool...and can then be re-gathered by the diver. You can't do that with ratchet reels.
Deployed from a deeper depth, the DSMB requires much less initial air to be added, than if it was deployed on the safety stop. A single breath into the bag at 20m is enough to deploy the bag due to air expansion on ascent. At 6m, the diver will need to add 3-4 full breaths...whilst holding down the bag...and not getting tangled. One of the big issues that causes concern with
shallow DSMB deployment is holding down a very buoyant bag, whilst coordinating the reel, line and yourself.
Deeper deployment is easier.
I recommend you seek instruction and practice practice practice before attempting this skill in a stressful situation.
It isn't
that hard.

However, it does take some practice to get it slick and easy. To the OP; be aware that there are lots of DMs who won't have a clue about this skill. I self-taught myself to do this (using the plethora of tutorial videos on youtube) and refined it over several thousand dives. It takes me about 10 seconds to deploy, inflate and release the bag now. The skills is easy, but needs to be coordinated and precise.
Most importantly...keep the line away from your body, so that it cannot snag anything when you release the bag.
1) Prepare the reel and DSMB.
2) Hold the reel furthest from the body, at arms length.
3) Add one full breath to the DSMB.
4) Hold the DSMB away from the body, at arms length.
5) Release the DSMB.