How is it correct to use "Qurashi" instead of "Qurayshi" for someone belonging to Quraysh, and is it correct to use "Mutairi" for someone belonging to the Mutair tribe?

In the case of nisba (attributive noun), the standard is to affirm the yāʾ, so one says "Qurayshī." However, its omission has been heard in eloquent Arabic, so one says "Qurashī." If the Arabs are heard to omit the yāʾ from the nisba for Muṭayr, then there is no objection to saying "Maṭarī." Al-Miṣbāḥ al-Munīr mentioned that one can form the nisba for Quraysh by omitting the yāʾ, saying "Qurashī," or by affirming it, saying "Qurayshī." Ibn al-Anbārī stated that the omission of the yāʾ in the nisba for Quraysh, Hudhayl, and Thaqīf is anomalous and not to be analogized from, and the eloquent usage is to affirm the yāʾ. Accordingly, both are eloquent usages, but affirming the yāʾ is more standard by analogy (aqyas), while omitting it is more frequent and eloquent.