Hi @fanis,
The effects you mention describe effects on the latent continuous variable assumed to underlie the ordered responses. With a probit link, the latent variable is a standard normal variable, and therefore the effects are on that standard deviation. You can’t go back from that to the 1-4 scale, which is not continuous. It should be sufficient to explain to your audience that the coefficients are on the latent variable, because it directly describes the predicted response probabilities.
An alternative is to describe the implied changes in probabilities at each response category as a function of the predictors. That is, you can obtain the predicted probabilities of each response category at different levels of your predictors, and then take their differences. For example, for a simple model with a single binary predictor and 4 levels of the response variable, this would give you four contrasts. If you have example data and code I might be able to put together an example of that if it sounds reasonable. A downside of it is that then you have four “effects” (and it will lead directly to thinking about category specific effects as described e.g. in the manuscript) to describe to your audience.
Does that help?