What the priest told you is in part correct and in part incorrect. The correct part is that, when the elements no longer have the appearance of bread or wine, Christ ceases to be present. If a drop of the precious blood has dried, it no longer has the appearance of wine, and so Christ is not present. This is historic Catholic teaching. Christ remains present only so long as the species of bread and wine maintain the appearances of bread and wine. That is the teaching of Thomas Aquinas:
If there be such change on the part of the accidents [appearances] as would not have sufficed for the corruption of the bread and wine, then the body and blood of Christ do not cease to be under this sacrament on account of such change, whether the change be on the part of the quality, as, for instance, when the color or the savor of the bread or wine is slightly modified, or on the part of the quantity, as when the bread or the wine is divided into such parts as to keep in them the nature of bread or of wine. But if the change be so great that the substance of the bread or wine would have been corrupted, then Christ’s body and blood do not remain under this sacrament, and this either on the part of the qualities, as when the color, savor, and other qualities of the bread and wine are so altered as to be incompatible with the nature of bread or of wine, or else on the part of the quantity, as, for instance, if the bread be reduced to fine particles or the wine divided into such tiny drops that the species of bread or wine no longer remain. (Summa Theologiae III:77:4)
Unfortunately, your priest is flat wrong about the correct thing to do when the precious blood spills. The Church mandates that the place be washed with water, diluting the precious blood so that it no longer has the appearance of wine and so that Christ ceases to be present, and then the water is to be poured into the sacrarium. It is not permitted simply to leave a spill alone until it dries. The General Instruction of the Roman Missal states: "If any of the precious blood spills, the area should be washed and the water poured into the sacrarium" (239).
It is not permissible to pour the precious blood itself into the sacrarium; only the water that was used to wash and dissolve the species under which the precious blood was present may be poured into it. The U.S. bishops’ document This Holy and Living Sacrifice forcefully states, "It is strictly prohibited to pour the precious blood into the ground or into the sacrarium" (38).