#Short answer: When the t is a part of stressed syllable, it often gets doubled (it's mostly true for verbs).

You can't tell which syllables are stressed by looking at the spelling. However, most dictionaries give phonetic transcription of words. You'll notice that there's a diacritic mark (') in the transcription, the syllable following that mark is stressed/ accented.

OP's examples:

• Committee /kəˈmɪt.i/ - The t gets doubled because it's a part of stressed syllable.
• Satisfy /ˈsæt.ɪs.faɪ/ - The t does not get doubled because it's a part of unstressed syllable.

#Explanation:

✴ When the t is a part of stressed syllable and is preceded by a vowel, it often gets doubled in present participle and past participle.

Examples: Submit has two syllables, the t is a part of the second syllable which is stressed so it gets doubled in present participle and past participle.

Submit /səbˈmɪt/ -> submitting, submitted.

Similarly, admit has two syllables in which the second one is stressed and the t is a part of second syllable so it gets doubled in present participle and past participle.

Admit /ədˈmɪt/ -> admitting, admitted.

✴ When the t is a part of unstressed syllable, it does not get doubled in present participle and past participle.

Examples: Elicit has three syllables. The t is a part of unstressed syllable so it does not get doubled.

Elicit /iˈlɪs.ɪt/ -> eliciting, elicited.

Similarly, interpret has three syllables. Stress is on the second syllable and the t is a part of the unstressed syllable so it does not get doubled in present participle and past participle.

Interpret /ɪnˈtɜː.prɪt/ -> interpreting, interpreted.

✴ Monosyllabic verbs that end with t can have -tt- or -t-, it depends on the preceding letter.

1. If the t is preceded by a vowel, the t often gets doubled in present and past participle.

Examples:

• Spot /spɒt/ -> spotted, spotting.
• Fit /fɪt/ -> fitted, fitting.
• Jot /dʒɒt/ -> jotted, jotting etc.

2. If a consonant precedes the t in monosyllabic word, the t does not often get doubled in present participle and past participle.

Examples:

• Act /ækt/ -> acted, acting.
• Want /wɒnt/ -> wanted
• Jolt /dʒəʊlt/ -> jolted, jolting etc.

✴ Multisyllabic verbs in which the t is preceded by a consonant sound have -t- in their present participle and past participle.

Examples:

• Accept /əkˈsept/ -> accepted, accepting.
• Attempt /əˈtempt/ -> attempted.
• Interact /ˌɪn.təˈrækt/ -> interacted, interacting etc.

For more details, read this answer.