The arrival of Columbus back to Spain was very noticed and ran as fast as the wind. Christopher Columbus, after having stopped in Lisbon, went to the village of Palos, from whence he had set sail on August the 3rd 1492 at 8 AM, where he arrived on March the 15th 1493. The Pinta arrived a bit later that same day.

By March the 22nd, the news of Columbus' success had reached the city of Córdoba, where in books of minutes of the council one can read the following: these gentlemen [the members of the council] saw a letter that Columbus had sent about the islands he had found, and the City commanded the messenger to be dressed and be given one thousand maravedis for the road

On March the 30th the Catholic Monarchs dispatched a letter to Columbus commanding him to come to the Royal Court at once, and this letter was a response to the one sent by the Admiral on March the 15th, as explicitly written: Don Christopher Columbus, our Admiral of the Ocean Sea, and viceroy and governor of the islands that have been discovered, we have seen your letters and had great pleasure in knowing what you told in them...

Columbus was in Seville by March the 20th, and according to Bartolomé de las Casas he had the intention of going to Barcelona by sea, as it would have been the fastest way to get there. However, the Admiral was enjoying his newly found fame, and had a change of heart, opting for the land route, showing all the peoples the animals, the Indians, and the many different things he had brought from across the great Ocean Sea. Las Casas gives a very sound but brief description of what kind of scenes one could see:

The Admiral departed from Seville with the Indians and all the rest. So much had the fame started to fly throughout Castile that new lands had been discovered, that were called the Indies, and so many peoples and so diverse, and that through this or that road came the man who had discovered them; not only from the villages through which he passed came people to see him, but villages remote to the road he used became empty and the roads became full in order to see him

When he arrived in Barcelona, he also incredibly well received, as he had become an Admiral, and was renowned as the man who had discovered the Indies. His recpetion in Barcelona by the Monarchs is attested by Gonzalo Fernández de Oviedo, Peter Martyr of Anghiera, and Ferdinand Columbus, who were all witnesses to Columbus' arrival. I will quote Ferdinand on this, as his version is a bit more complete:

He came to Barcelona in mid-April [...]. The Monarchs commanded he be solemnly received. To his encounter came everyone in the city and the Court; and the Catholic Monarchs waited for him publicly seated, with all dignity and majesty, in a most rich throne with a canopy in gold brocade. He was there with such honour and favour from Thei Highnesses that when the King rode through Barcelona he would be by his side

Let's not forget that by the time Columbus made it to Barcelona, the news of his arrival, thanks to the letters he sent to Luis de Santángel and Gabriel Sánchez, were already circulating for good. By the last week of March of 1493, his letter was printed in Barcelona by Pere Posa in Spanish and in Catalan. By the date he arrived to the city (April 20th according to León Guerrero and Rumeu de Armas), the news of his journey to the Indies and back were already being translated to Latin in Rome, were they would be published on April the 29th as stated in the explicit of Silber's edition. The news had reached Rome by April the 18th, as documented by the Compendio della Cronica Delfina: For letere di Roma del legato con avisi avuti di Portogallo de le insule che hanno trovato le barge del re, che andono in India, e la lettera é data in la charavella sopra l'xola di Canaria a di 13 fevrier pasado [There were letters of the legate from Rome with news from Portugal of the islands that have been found the King's ships that go to India, and the letter is dated on the island of Canary on February the 13th].

So, in essence, yes, Columbus became a celebrity in his own right, and there was much fanfare both in Barcelona where the Court was, and in every place on the way from Palos to the Catalan city