On the topic of Clovis' conversion, more can be said and asked, bu you might be interested on this post about Why did clovis converted to Catholicism instead of Arianism like most other Germn kings?

As for the Battle of Tolbiac there's, as for many aspects of Clovis' reign, a lack of sourced details.

The most known is Gregory of Tours', where the hagiographic tale of the royal conversion is found (and written with Constantine's conversion story in mind) but otherwise bare-bone : there's no date, and we only know from a later mention that the battle was at Tolbiac and that Sigebert the Lame was wounded there. Eventually, as a consequence of divine grace Clovis obtained by praying to the Christian god, Gregory quickly passes over its consequences in a frustratingly short description : "As he said this [praying to the Christian god] the Alemanni turned their back and began to rout; and seeing that their king was dead, they surrendered to Clovis."

Another source, the Life of Saint Vaast by Jonas of Bobbio (II), doesn't give much more informations on the battle itself (essentially following in Gregory's footsteps), but give us some information about its prelude and especially Clovis' initial plans in fighting the Alemanni : bypassing the Rhine north of Tolbiac and not engage directly their army. As it failed, it might explain the severe difficulties encountered by Franks (especially if Sigebert, whose role is never mentioned, couldn't support his ally) before Clovis' skills and the good fortune of having the enemy king died helped him.

Indeed, Theodoric's letter to Clovis (MAG, Variae XII) to require him to display moderation (and implicitly do not push his advantage in trying to dominate Alemanni that were client to Theodoric) also confirms that the Alemmanic king died, causing the rout of his people ("It should be enough for you that the pride of this people fell with their king"). Interestingly, though, as it is not dated and as there's a case that it wasn't the only Frankish campaign against Alemmani who displayed "an excess of perfidy", with the implication they already were submitted once and tried to shake it off) : but Gregory of Tours' account is not dated either (and possibly either just keeping "one" or mixing them for simplicity's sake, as the History of Franks is in itself as summary of the original work).

As far as the Battle of Tolbiac can be known, which is difficult giving the hagiographic nature of Gregory and Jonas' work as well the laconism of Theodoric and the possible existence of several campaigns against Alemanni, the explanation to Alemanni's rout seem to be the dead of the king that led the army. It's not particularly implausible; early medieval kings had an important military function whose warring performance was important in keeping a moral leadership and cohesion : the Battle of Vouillé some years later saw the Visigothic army defeated and routed as Alaric II died in the initial shock.

Reading Gregory, it is difficult to assert whether the Alemannic king died and the leaderless troop engaged in a retreat that became a rout; or if Alemannic engaged in a tactical retreat before (maybe caused by Clovis regaining control of the situation, thanks to otherwise known military skills) that only became a rout as the king died. But this, as far as sources goes, seems to be the key of the battle.