Rubiales has been provisionally suspended by FIFA after refusing to resign over the incident. Rubiales pulled Hermoso towards himself and kissed her on the lips while she collected her winners' medal after beating England last Sunday.
Hermoso stressed on Friday she did not consent to the kiss and the fallout from incident continued on Saturday afternoon as Spain women's coaching staff resigned en masse - though Vilda did not.
In a statement published in Marca, Vilda said: "The events that have taken place since Spain won the Women's World Cup for the first time in its history...have been a real nonsense and have generated an unprecedented situation, tarnishing a deserved triumph of our players and our country.
"I deeply regret that the victory of Spanish women's football has been harmed by the inappropriate behaviour that our until now president, Luis Rubiales, has carried out and that he himself has acknowledged.
"There is no doubt that it is unacceptable and does not reflect at all the principles and values that I defend in my life, in sport in general and in football in particular. A clearly undesirable climate has been generated, far from what should have been a great celebration of Spanish sport and women's sport.
"My work as the women's national coach and sports director of the women's national team has always been aimed at achieving sporting success, but also at promoting initiatives that promote inclusion, respect and equity. I reiterate my unwavering commitment to promoting a sport that is a model of equality and respect in our society."
Spain assistant managers Montse Tome, Javier Lerga and Eugenio Gonzalo Martin were among those to have decided to stand down from their positions.
Physiotherapist Blanca Romero Moraleda and goalkeeper coach Carlos Sanchez, plus half a dozen others at several age-group levels, have also tendered their resignations.
A statement from the coaches said: "The undersigned express their firmest and most emphatic condemnation of the conduct shown by the president of the Spanish Football Federation. He offered a story that does not reflect in any way any of the feelings of Jenni Hermoso, who has expressly stated that she felt 'victim of aggression'.
"The technical team supports the player Jennifer Hermoso, endorsing the version offered by her. In light of the unacceptable attitudes and statements made by the top leader of the RFEF, the undersigned have made the decision to relieve themselves of their duties."
FIFA, which opened disciplinary proceedings against Rubiales on Thursday, announced on Saturdat in a statement the 46-year-old official was banned "from all football-related activities at national and international level" for an initial period of 90 days.
Jorge Ivan Palacio, the chairman of the FIFA disciplinary committee, has ordered Rubiales and the RFEF (Spanish FA) to refrain from contacting or trying to contact Hermoso, either directly or through intermediaries.
Hermoso accused the RFEF of a "manipulative, hostile and controlling culture" as a total of 81 players signed a letter stating they will not accept national team call-ups while Rubiales remains in situ.
Rubiales insisted in his speech on Friday he had been the target of a "social assassination" and repeatedly and emphatically stated "I will not resign", words that drew applause from the gathered delegates at an extraordinary general assembly of the RFEF.
Rubiales claimed the incident was "spontaneous, mutual, euphoric and consensual" but Hermoso, who previously suggested comments playing down the incident attributed to her by the federation were false, hit back with an attack on the organisation as a whole.
"It is not up to me to evaluate communication and integrity practices, but I am sure that as the world champion national team we do not deserve such a manipulative, hostile and controlling culture," she said in a statement on Twitter on Friday.
"I want to reinforce the position I took from the beginning, considering that I do not have to support the person who has committed this action against my will, without respecting me, at a historic moment for me and for women's sport."
Additional reporting by Press Association.