The Pali dictionary I use say Attavāda means the theory of a soul? Is that correct ?
Inherently it means that there is an independent self/soul that exists without any causes or conditions, which is a form of magical thinking.
Whereas as an Ariyan does not believe in anything that exists independently, without any causes or conditions.
Things cannot be born of a “self”, because there is no “self” that causes things to happen, instead your intentions, body, feelings, consciousness, perceptions, etc… all Dependently Originated, which means they arise and cease due to causes and conditions and are not caused by a “self” or “soul”.
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Attavada is most prominently found in Dependent Origination, as follows;
There are these four kinds of grasping.
Cattārimāni, bhikkhave, upādānāni—
Grasping at sensual pleasures, views, precepts & observances and theories of a self.
kāmupādānaṁ, diṭṭhupādānaṁ, sīlabbatupādānaṁ, attavādupādānaṁ
SN 12.2
It seems to obviously mean grasping in the form of self-beliefs. The idea of ‘theory of soul’ seems far too limited in scope. 
Then he said to them, “My soul is overwhelmed with sorrow to the point of death. Stay here and keep watch with me.”
What Jesus says is that he is sad. So previously “soul” and “self” were more or less synonymous. But presently “soul” is not very popular word, and may mean “it is what some Christians believe but we aren’t so naïve” while even a Buddhist, as long he is a puthujjana is a victim of sakkayaditthi, inseparable from attavada. Therefore even usage the word “theory” in that definition is wrong, since one doesn’t have a theory about oneself, self-image has nothing to do with theory.
Nanavira Thera:
The P.T.S. (London Pali Text Society) Dictionary, for example, supposes that the word attā in the Suttas refers either to a phenomenon of purely historical interest (of the Seventh and Sixth Centuries B.C.) known as a ‘soul’, or else to the reflexive ‘self’, apparently of purely grammatical interest. All suggestion that there might be some connexion (of purely vital interest) between ‘soul’ and ‘self’ is prudently avoided.
Sounds like his “heart” or “citta”.