This reaction is an example Barbier reaction (Ref.1), which was discovered by Philippe Barbier who was the teacher of Victor Grignard, the discoverer of Grignard reaction. The main difference other than metal used between Barbier and Grignard reactions are the former is one-pot reaction while the latter is two pot reaction as ref.1 states:
A synthesis with the aid of an organometallic compound is usually carried out in two steps: 1) the organometallic reagent is prepared from an organo halide and a metal in a solvent, 2) a chosen substrate is added to this reagent. In a Barbier reaction these two steps are combined: a mixture of the organo halide and the substrate is added to a suspension of the metal-in an appropriate solvent.
The other differences include ability to use water as the solvent, making it more greener (Ref.2). First, the allyl halide reacts with metallic $\ce{Zn}$ to give the corresponding allyl zinc species, which then reacts with a ketone or aldehyde (the electrophile) to give corresponding alcohol (nucleophilic addition). Therefore, your first suggestion is not correct. The correct major product is the second one (Ref.3 & 4):
I said it is the major product, because the conjugate addition predominate under these conditions and with certain allylic or propagyl halides as given in the following example (Ref.4):
When $\ce{R = H}$, product $\bf{II}$ predominates while when $\ce{R = n-Hexyl}$, both products, $\bf{I}$ and $\bf{II}$, formed in significant yields (Ref.4). This suggest that the nucleophilic addition to carbonyl compound is the slower step and therefore, attack on more stable carbocation would predominates. In your case, it is secondary allylic carbocation over initial primary allyl carbocation. Also, considering resonance structures of the initial carbocation, the larger contributors are secondary and primary allylic carbocations because they are more stable than the other contributor, secondary cyclohexyl carbocation. The appearance of the product through that carbocation is based on the reaction rates of nucleophilic addition.
However, keep in mind that the regioselectivity of this reaction is highly dependent on the nature of the alkyl halide (usually, allyl or propargyl halides) and carbonyl compound, steric hindrances, solvent effects, and the metal used (note that Barbier reaction uses other metals such as $\ce{Zn, Sn, In, Sm}$, etc.).
References:
- Cornelis Blomberg, In The Barbier Reaction and Related One-Step Processes; Springer-Verlag: Berlin, Germany, 1993 (ISBN: 978-3-540-57169-8).
- Feng Zhou and Chao-Jun Li, "En route to metal-mediated and metal-catalysed reactions in water," Chem. Sci. 2019, 10, 34-46 (DOI: 10.1039/C8SC04271C).
- Tak Hang Chan and Chao Jun Li, "Organometallic reactions in aqueous medium. Conversion of carbonyl compounds to 1,3-butadienes or vinyloxiranes," Organometallics 1990, 9(10), 2649–2650 (DOI: https://doi.org/10.1021/om00160a008).
- Artur Jõgi and Uno Mäeorg, "Zn Mediated Regioselective Barbier Reaction of Propargylic Bromides in $\ce{THF/aq_. NH4Cl}$ Solution," Molecules 2001, 6(12), 964–968 (DOI: https://doi.org/10.3390/61200964).