I think you're just hearing the lack of aspiration; English and German "t" is generally aspirated at the start of a syllable, while Spanish and Italian generally lack aspiration on voiceless plosives (but their voiced plosives start their voicing earlier). (For a more detailed comparison of English and Spanish plosives, see The Sounds of Spanish,
by José Ignacio Hualde.) These differences are related to voice onset time. In the International Phonetic Alphabet, we can indicate aspiration with a superscript ʰ after the letter for a regular voiceless consonant, so the sound at the start of English "ten" can be writen as [tʰ].
Unaspirated (also called tenuis) voiceless stops are quite common and found in many languages.
Some languages, such as Hindi and Ancient Greek, contrast voiceless aspirated plosive phonemes ([pʰ], like in English "pin"), voiceless tenuis plosive phonemes ([p], like in English "spin" or Spanish "pollo"), and voiced plosive phonemes ([b], like in Spanish "bello").
(I used the example of "p" rather than "t" because Hindi actually has two types of "t/d" sound, dental and retroflex. In fact, Hindi also has one more type of phonation: the "voiced aspirate" or "murmured" plosives, represented by appending ʱ to a voiced plosive symbol.)