Your question contains a wrong assumption. You take for granted that Evenki čoolii 'tongue' is considered a descendant of PTg *xilŋü 'tongue' together with its synonym inńi, but this is not the case. These words come from two different roots. Evenki čoolii is probably a deverbal noun from a root meaning 'to gossip, chat, babble', and has a parallel in Negidal čoolïï- 'id.' (SSTM 2: 405), while Evenki inńi < PTg *xilŋü.
If you take a closer look at the page dedicated to *xilŋü on Wiktionary, you will realize that it does not list čōlī under this root. The only forms cited are Evenki inńi, Oroqen (sic) iŋi, Nanai siŋmu, Orok sinu and Manchu ilenggu. I suspect iŋi is really an Oroch word mislabelled as Oroqen. To these, we might also add Even jenŋä, Solon iŋi, Negidal ińŋi, Udihe iŋi, Ulch sińu and Jurchen 亦冷吉 *(h)ilenggi, or *(h)ilenggu (see Kane 1989: 315, #885). In Nanai, the doublet sirmu is attested in the Kur-Urmi subdialect (SSTM 1: 136-37). The reconstruction *xilŋü was developped by Sergej Starostin, Anna Dybo and Oleg Mudrak (2003), the same authors of the highly controversial Altaic Etymological Dictionary. Their reconstruction of Proto-Tungusic is heavily based on Cincius' (1949) previous ideas and on her two-volume etymological dictionary of Manchu-Tungus (1975-77), but here and there they take into consideration some of Benzing's (1955) alternative proposals.
Setting aside the complicated history of the Tungusic vocalism, I would say the proto-form *xilŋü is acceptable, because it is based on a couple of well-established facts about Proto-Tungusic phonology, such as the existence of the spirant *x phoneme and the reflexes of the cluster *lŋ. Initial *x is systematically lost in the Northern (Evenki, Even, Negidal, etc.) and Transitional (Udihe and Oroch) branches, while is preserved in Southern Tungusic (Nanai, Orok, etc.), though only partially in Jurchen and Manchu. Its reflexes are x-, or s- before a front vowel (like in this case) in Nanai, Orok and Ulch, as you can see in the second paragraph. The consonant cluster *lŋ evolves as ńŋ, nŋ, or simply ŋ, in most languages through partial assimilation of the lateral element to the following nasal. However, Tugur-Chumikan and Ayan dialects of Evenki, which have ilŋi beside Standard Evenki inńi and Barguzin Evenki ińŋi, show a more direct evidence of the original *l of the cluster. The same can be said for Kur-Urmi Nanai sirmu, which substitutes a rhotic for the lateral.
Turkic *til ~ *tïl 'tongue', Mongolic *kelen 'id.' and Uralic *käle 'id.' have nothing to do with Tungusic *xilŋü, despite the superficial phonetic similarity. By the way, the Chuvash form is čĕlxe, not **čelxe, and the Yakut one is tïl, not **tol (see Räsänen 1969: 478). Same for Amur, North Sakhalin and East Sakhalin Nivkh hilx 'tongue'. You would need a fair amount of comparative gymnastics in order to argue for their cognacy, and the required phonetic changes would be in any case unsystematic (by which I mean they would most likely be valid only for the word for 'tongue').
When reasoning about similarities and common patterns across languages, you should resist the tentation of thinking that two or more languages are related to each other just because they (or their ancestors) have one or two words that sound similar. Keep in mind Occam's razor: you should sift through alternative explanations that are much simpler before postulating the existence of a macro-family of languages. As for the word for 'tongue', the fact that it often contains the sounds /l/ or /d/ and /k/, /g/, /x/ or /ŋ/ in many languages may be due to phonosymbolism. Such sounds exemplify the full range of mobility of the tongue, i.e. /l/ and /d/, being alveolar, are the most advanced sounds the tongue can produce, while /k/, /g/, /x/ and /ŋ/, being velar, are the most retracted. In this sense, it is almost like the forms /lVk/, /dVŋgV/, /kVlV/, etc. display a deictic gesture, and therefore, by virtue of such extra-linguistic property, they end up being quite common in natural languages, but they do not constitute evidence for a genetic relationship.
Benzing, Johannes. 1955. Die tungusischen Sprachen: Versuch einer vergleichenden Grammatik. Wiesbaden: Verlag der Akademie der Wissenschaften und Literatur in Mainz.
Cincius, Vera I. 1949. Sravnitel’naja Fonetika Tunguso-Man’čžurskix Jazykov. Leningrad: Izdatel’stvo «Nauka».
Kane, Daniel. 1989. The Sino-Jurchen Vocabulary of the Bureau of Interpreters. Bloomington: Indiana University.
Räsänen, Martti. 1969. Versuch eines etymologischen Wörterbuchs der Türksprachen. Helsinki: Suomalais-Ugrilainen Seura.
SSTM = Cincius, Vera I. (ed.). 1975-1977. Sravnitel’nyj slovar’ tunguso-man’čžuskix jazykov, Materialy k ètimologičeskomu slovarju. Vols. 1-2. Leningrad: Izdatel’stvo «Nauka».
Starostin, Sergej A., Dybo, Anna V. and Mudrak, Oleg A. 2003. Etymological Dictionary of the Altaic Languages. Leiden: Brill.