So Geshe Sonam states that when one visualizes the merit field the central figure varies but it is understood to be inseperable from one's guru, hence the name "guru-deity" or "guru-yidam". He told me that when Lama Tzongkhapa was still alive his students would have been visualizing him in the centre of the merit field because one's guru is an ideal object for prostration/worship as it is through them that we have access to the precious teachings. Whether they visualized Lama Tzongkhapa in his yellow hat form, for example, or perhaps visualized a figure of Buddha Shakyamuni with the understanding he was inseparable from LTK, I am not sure. It is interesting to note that many practices within the Gelug, for example the Jorcho or Preliminary Practice, still have Buddha Shakaymuni as the main figure.
According to my research, in terms of the liturgies that were developed with Tsongkhapa as the central figure, at least one seems to have been composed just shortly after Lama Tzongkhapa left his body. The principal ones in use and as daily practices of Gelugpas are the Lama Chopa/Guru Puja and the Ganden Lhagyama/Hundreds of Deities of Tushita practices.
The Lama Chopa was composed by Panchen Lama Losang Chokyi Gyaltsen, whose dates are 1570-1662, so this text must have been composed at that time. There is a wonderful commentary by Kachen Yeshe Gyaltsen that is only available in Tibetan at the moment, but I understand there is a translation by David Gonsalez in the works. In this liturgy the central figure is a large Tsongkhapa, with a small Shakyamuni Buddha and smaller Vajradhara at his heart. This liturgy is considered extremely important by all the major Gelug masters, HH Dalai Lama mentions it is very precious because it contains a way to combine the practice of the three important deities: Yamantaka, Guyasamaja and Chakrasamvara (Heruka).
The practice of Ganden Lhagyama was composed by Dulnagpa Palden. It is a practice that integrates the seven limbs with a short guru yoga of Lama Tzongkhapa and recitation of his mantra. There is less information about the author of this text on the web, but it seems he was co-founder, along with his master Je Sherab Sengye, of Segyu Monastery in 1432. Lama Tsongkhapa passed away in 1419 so this text would likely have been composed very soon after. It involves a visualization of Tsongkhapa with his two main disciples in the form of lamas wearing the yellow hat.
So, short answer, students of LTK would have meditated on his as the guru-deity even while he was still alive, but I could not confirm that this was in the yellow hat form, perhaps it was Shakyamuni but knowing that he was "inseparable" from LTK. The first liturgy visualizing Tsongkhapa in his actual form can likely be dates to the early or mid 1400s, so probably very shortly after he passed away.
In order to ensure my mind never comes under the power of the self-cherishing attitude,
I must obtain control over my own mind.
Therefore, amongst all empowerments, the empowerment that gives me control over my mind is the best,
and I have received the most profound empowerment with this teaching.
brtsal ba'i bkhra drin