As suspected by alephzero, the word "tono" (in Spanish) or "tom" (in Portuguese) refers in this context to the "church modes", i.e. the Gregorian modes of the plainchant tradition.
In The Evolution of Organ Music in the 17th Century: A Study of European Styles, John R. Shannon describes Musical Flowers for keyboard instrument and harp, the chef d'ouvre of the Portuguese composer Manuel Rodriguez Coelho published in 1620, as "... a well-organized anthology containing the following: twenty-four tentos, three each of the eight church modes;[...]" (p.130).
The tentos in the collection are named in succession "First tento of the first tone", "Second tento of the first tone", etc up to "Third tento of the eight tone" (the scores are available on line here).
The eight tones would be the 4 authentic and 4 plagal Gregorian or church modes, but as the French Baroque Organ Music and the Eight Church Tones paper referenced by alephzero points out, "in many pieces the tonal structures or keys seem to bear little relationship to those of corresponding plainsong tones". For example, the practice of applying a G minor "key signature" to pieces in the second tone is present in Coelho's work:
("IV. First tento of the second tone")
As well as different keys (e.g. D major) for the seventh tone (although not adopted as a "key signature", the accidentals place the piece clearly in that tonality):
("XIX. First tento of the seventh tone")
So judging by the example of Coelho's work ("the first monument of 17th-century Iberian keyboard music" according to Shannon), there seems to be great consistency between Iberian practice and that described in the paper about French Baroque organ music.