Alwars (in pure Tamil "AzhwAr") means "One who immerses himself". They really, deeply immersed themselves in their devotion and bhakti towards the Lord Sriya: Pathi Sriman Narayanan. The AzhwArs are reported to be incarnations of NithasUris of Sri Vaikuntam, namely, the weapons, the Vanamaali, the GarudA, et al. They lived like human beings and burst out bhakti laden great works for the sake of humanity. The works of Alwars stood mysteriously a replica of the Vedas themselves and therefore came to be known as Dravida Veda. In fact, there is a view that even the great Rishis are no match to the greatness of the Alwars because these Rishis got their 'jnAnam' ( wisdom) as a result of their own actions of 'spiritual merit' ( Punyam) whereas the wisdom of the Alwars was the direct result of the Lord's divine grace and therefore called ' Divyam'. It is because of this that the works of Alwars is called ' Divya Prabandham' are 4000 poems (pAsurams).
These works of AzhwArs are non-paralleled in every sense- be it in sentiment, style or syntax.They take even a casual reader on a guided tour into the esoteric exegesis of the Vedas without offending the provisions of exclusions and prohibitions enjoined in the study of the Vedas in original
you are right...read in the ASI website description that - The epithet Alvar is taken to be one of respect. It may also indicate that the person was dead at the time!!