In your examples, the production labeled "voiced glottal fricative" is 2/3 voiceless glottal fricative with the right 1/3 being voiced, followed by a very long schwa. The percept of schwa can be explained because most of what you hear is schwa.
There is a similarity between schwa and h, that they are often characterized as "neutral state" segments, because they don't have characteristic oral cavity articulatory gestures that other consonants and vowels have. Schwa is neither front nor back, high nor low, and h has no oral cavity constriction, instead it takes on whatever tongue position the surrounding vowels have and only contributes a breathy laryngeal source.
In any sustained consonant, the tongue has to be somewhere. That position is usually where schwa is, unless the consonant demands a different position (e.g. [s]). It is possible to produce [φ] with the tongue in the position of [i, æ, ɑ], but it is not normal to do so – also, because of the constriction formed by [φ], you have a hard time hearing the difference. With [h], there is no supraglottal constriction because of the consonant, so you can clearly hear the neutral schwa-like tongue position that you assume when you try to produce just [h].