'Quiet' refers to a particular glissando (i.e. a slide from one note to another) that first appears in Undertale 's Quiet Water, and is referenced in Deltarune 's Quiet Autumn.
('Quiet', as heard in Quiet Water)
While the leitmotif itself is very limited in its use, the Undertale and Deltarune soundtracks make great use of the general musical device of rising arpeggios and glissandos, using them to evoke a variety of emotions.
This article will first cover the 'Quiet' motif, before exploring some (but not all) of these other examples.
Although not quite identical (it's more of a rising arpeggio), context implies it is indeed an intentional reference.
The naming convention of 'Quiet [noun]' is preserved, the instrumentation is very similar, the motif's usage underneath a simplified form of another leitmotif is similar, and both tracks play in 'rest areas'.
As an aside, note how after two repetions, the quote is transposed down a whole tone.