1. The confusing thing here is that the contradiction to which the Gemara refers is a contradiction between two statements of Rebbi Yochanan, but since, according to Abaye, the two statements of Rebbi Yochanan are both based on the opinion of Rebbi, in effect there is a contradiction in Rebbi's words. However, Rebbi's opinion is one and the same: "Linah Mo'eles b'Kidush Yadayim v'Raglayim" -- after the entire night has passed by, the Kohen must wash his hands and feet again (Beraisa, 19b).

2. The contradiction in Rebbi Yochanan's words is as follows. The Gemara (21a) cites Rebbi Yochanan's opinion that once one has submerged the Kiyor into the well shortly before sunset, as is the Mitzvah to do so, one may not bring the Kiyor up again all night long. The Gemara (beginning of 21b) explains that this is because of "Gezeiras Shiku'a" -- if one were to raise up the Kiyor during the night in order to wash for the Avodah during the night, one might forget to submerge it back into the well before daybreak, and thereby the water would become invalid for Kidush Yadayim v'Raglayim for the following day. This ruling of Rebbi Yochanan follows Rebbi's opinion (because, according to the dissenting view of Rebbi Eliezer b'Rebbi Shimon (19b), the passing of the night does not invalidate the Kidush Yadayim v'Raglayim).

3. The Gemara (beginning of 21b) now poses a contradiction in Rebbi Yochanan's position. Rebbi Yochanan made another statement: if one washed one's hands for the Terumas ha'Deshen (which is performed shortly before daybreak), he need not wash again at daybreak. The Gemara states that according to Rava (who is first mentioned at the end of 20a), there is no contradiction between the two statements of Rebbi Yochanan, because the statement of Rebbi Yochanan mentioned above (in 2.) follows the opinion of Rebbi, while the statement of Rebbi Yochanan mentioned now follows the opinion of Rebbi Eliezer b'Rebbi Shimon. However, according to Abaye, there is a problem. Abaye (end of 20a) said that the second statement of Rebbi Yochanan also follows Rebbi. Since we just learned that Rebbi Yochanan maintains that there is a "Gezeiras Shiku'a" (i.e., one never raises up the submerged Kiyor during the night), why does he not say that if the Kohen washed his hands before the Terumas ha'Deshen, he should make sure to return the Kiyor to the well immediately after Kidush Yadayim? (See Rashi DH Ela l'Abaye, and emendments of the Tzon Kodashim #3 and Gertner edtion.)

4. In short, according to Abaye, the two statements Rebbi Yochanan both are in accordance with the view of Rebbi.

Kol Tuv,

Dovid Bloom