The "th" pronunciation of the letter "z" is how Spanish speakers in Spain pronounce the letter. So, someone in Spain would refer to the island as "Ibitha," even though they'll still spell it as "Ibizia." This would actually make it the original pronunciation. Considering that Spain and Great Britain are neighbors, they are likely to say it the same way.
In Spanish, the "th" sound is used for the letter "z" mostly in Spain. In North and South America, Spanish speakers usually pronounce the letter the same way as the letter "s." For example, a Latin American Spanish speaker would pronounce "taza" as "ta-sa," while one from Spain would say it as "ta-tha."
Just as someone native to the U.S. would speak English differently than someone born in the U.K., someone born in a Latin American country will speak Spanish differently. This has to do with the fact that languages are constantly changing, and factors such as distance cause different accents.
Whether you pronounce it as one or the other depends on whether you want an accent closer to Latin America Spanish or Spain Spanish. Most people who live in the Americas use Latin American pronunciation.