Mysql – Does MySQL reindex on update

I have a users table with various fields which are getting updated frequently.
i.e table have:

userid -  PRIMARY int
profile_views - int
ratings - int
last_active - int ( to store UNIX timestamps for sorting purpose)

I also have an index on last_active to get the last active users. When user logins or performs a certain action last_active gets updated and same with profile_views and ratings.

My question is does mysql reindex all table ro reindex index last_active when I update last_active index value or update profile_views or ratings?

table:

CREATE TABLE IF NOT EXISTS `users` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `ip_address` varbinary(16) NOT NULL,
  `username` varchar(100) NOT NULL,
  `password` varchar(80) NOT NULL,
  `salt` varchar(40) DEFAULT NULL,
  `email` varchar(100) NOT NULL,
  `title` varchar(255) NOT NULL,
  `detail` varchar(500) NOT NULL,
  `genre_id` int(2) NOT NULL,
  `category` tinyint(1) NOT NULL,
  `profile_views` int(11) NOT NULL,
  `ratings ` int(11) NOT NULL,
  `last_active` int(11) NOT NULL,
  PRIMARY KEY (`id`),
  KEY `genre_id` (`genre_id`),
  KEY `last_active` (`last_active`)
) ENGINE=InnoDB  DEFAULT CHARSET=utf8 AUTO_INCREMENT=4059 ;

and second table to join to

CREATE TABLE IF NOT EXISTS `users_genre` (
  `userid` int(11) NOT NULL,
  `genre_id` int(11) NOT NULL,
  KEY `userid` (`userid`),
  KEY `genre_id` (`genre_id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

Thanks