Are /t, p, k/ aspirated when they are at the start of a syllable after another syllable that ends in /s/?

Unfortunately, there is no definitive answer to a question about pronunciation in English because the pronunciation of any given word varies enormously from speaker to speaker. Moreover, syllabification is a highly controversial topic because of the following reasons:

• there are many different approaches to syllabification in English
• syllabification varies across idiolects¹
• there isn't a widely agreed on syllabification rule
• most syllabification rules have lots of exceptions

Also, you say ‘voiceless plosives such as /t/, /p/ and /k/ are produced with a strong burst of air when they are in the start of a syllable before a vowel’; I don't agree entirely because for most speakers, it is at the start of a stressed syllable.

Words like whisper, sister and whiskey can be syllabified in many different ways. Some of the syllabification rules are:

Ambisyllabicity

Some linguists (such as Kahn²) think that the /s/ is ‘ambisyllabic’, meaning it belongs to both the preceding and the following syllable simultaneously. In his Syllable Structure: The Limits of Variation, San Duanmu has represented ambisyllabic consonants by underlining them. Other linguists represent them by transcribing them in {curly brackets}. I'll represent them by transcribing them separately with both the preceding and the following syllable for the sake of clarity:

• whisper → [ˈwɪs.spə]
• sister → [ˈsɪs.stə]
• whiskey → [ˈwɪs.ski]

As the plosives are preceded by an /s/, they should be unaspirated, according to this analysis.

Maximal Onset Principle

According to MOP³, intervocalic consonants are syllabified as the onset of the following syllable as long as it doesn't violate the Phonotactic constraints. It would mean that VCV has to be syllabified as V.CV.

However, if you syllabify whisper, sister and whiskey as /ˈwɪ.spə/, /ˈsɪ.stə/ and /ˈwɪ.ski/ respectively, there's a violation of the Phonotactic constraints; stressed lax vowels—/ɪ, ʌ, ɒ, ʊ/—cannot occur syllable-finally i.e. there should be a consonant after those vowels, so whisper, sister and whiskey are syllabified as:

• [ˈwɪs.pə]
• [ˈwɪs.ki]
• [ˈsɪs.tə]

According to this analysis, the plosives are syllable-initial which suggests that they should be aspirated; however, in practice, they are not aspirated as strongly as they would be in the beginning of a stressed syllable (cf. distaste, discomfort).

Wells' syllabification

Prof John Wells proposes a different syllabification theory⁴. He says that ‘consonants are syllabified with the more strongly stressed of two flanking syllables’. John Wells syllabifies⁵ whisper, sister and whiskey as, respectively:

• [ˈwɪsp.ə]
• [ˈsɪst.ə]
• [ˈwɪsk.i]

He syllabifies the plosives with the coda of the first stressed syllables. And voiceless plosives in codas are usually unaspirated. So according to him, the [p, t, k] in the above examples are unaspirated.

Further observations

• Some native speakers don't aspirate plosives at the start of a syllable following another syllable that ends in an /s/ so long as the the word is monomorphemic (having a single morpheme as in whiskey).
• Some native speakers aspirate voiceless plosives across morpheme boundaries, for example, dis.taste.
• Most, if not all, native speakers aspirate plosives across word boundaries as in this time
• There are also some speakers that don't aspirate plosives across morpheme boundaries when preceded by an /s/ even if they're stressed, so the first /t/ in dis.taste might be pronounced without aspiration
• Most speakers do not aspirate plosives in unstressed syllables

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Notes and references

1. Idiolect means ‘the language or speech pattern of one individual at a particular period of life’. ^{[Merriam-Webster]}
2. Read this paper (25 - Ambisyllabicity in English: present and past) for Kahn's ambisyllabicity
3. I've explained MOP in this answer to another question
4. Syllabification and Allophony - UCL
5. Those transcriptions are from Wells' Longman Pronunciation Dictionary