Handbook of Liturgical Practice of the Russian Church Abroad
It is often observed that as they are coming forward to kiss the Cross in the Priest’s hands at the conclusion of the Divine Liturgy, the faithful first go to venerate one or more of the holy icons that are ‘en route’ to the Priest’s position on the amvon, venerating these before they come to him. The Priest should instruct his flock that this is not proper: when it is present amongst other icons, we always venerate the Cross first. This includes the conclusion of the Divine Liturgy. The faithful should first come to the amvon to venerate the Cross in the Priest’s hands, waiting patiently for their turn to do so without venerating other icons first, and only after they have kissed the Cross and received antidor (and then listened to the post-Communion prayers, if they have communed), should they then go about venerating holy icons within the temple.
EXPLANATORY NOTE: In the oldest tradition of the Church, faithful do not venerate any icons immediately after partaking of Holy Communion, before or after kissing the Cross, out of an ongoing reverence for the fact that they have just received into their bodies the One to Whom all icons point, and as piously extolling that experience as above all veneration — a full participation. In this older custom, only the Cross is kissed at the end of the Liturgy; no icons are venerated at all until the liturgical day comes to its end, i.e. at the service of Vespers that evening. Thus the whole day is liturgically centred around the receipt of Communion.
However, as in most parish settings the faithful are not in the temple for Vespers on Sunday evening, but return home after the Liturgy and a meal, this older tradition has been modified into the present practice. Nevertheless, we maintain the order always maintained in the temple, namely that the Cross is venerated before holy icons.