A letter of ogham is fixed by two facts: its family, and how many strokes it carries.
How the letter is formed
Tinne is the third letter of the second family, Aicme hUatha, and is cut as three strokes on that family's side of the line, the side opposite the first family's.
The order of the alphabet is not the Latin order
The ogham sequence begins B, L, F, S, N, then H, D, T, C, Q. That is not alphabetical order in any Latin sense, and it is not obviously phonological order either. The arrangement is one of the standing problems of the subject: proposals range from a deliberate scrambling of a Latin model, to a grouping by articulation, to an order inherited from a source that has not survived. No proposal has carried the field.
The atlas records the order as attested and the explanations as competing, because that is the state of the scholarship rather than a gap in the record.
The sound
Tinne carries the value T. It appears throughout the surviving inscriptions, which are overwhelmingly personal names in the genitive case, cut on standing stones in Ireland and in Irish-settled parts of Wales, Scotland and the Isle of Man, dated on linguistic grounds to roughly the fourth to sixth centuries.
The holly attached to this letter comes from the later manuscript tradition and is treated separately here.